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[ Lord 




H o n to o n 



The A' /!>/// of Translation and Reproduction is Reserved 






A LARGE part of this volume was already in 
print when it was decided, and promised in the 
Preface to Vol. I., that the second volume should 
include subjects connected with Geology, and the 
third should be chiefly concerned with Maritime 
affairs. Accordingly, two hundred pages on 
navigational subjects were marked " Vol. III." 
and struck off before any progress was made 
with Vol. II. Hence Vol. III. now appears 
before Vol. II., the publishers having advised me 
that they would not be professionally shocked 
by such an irregularity. The present volume 
ends with an article kindly contributed by Capt. 


Creak, R.N., on a subject of great navigational 
importance, disturbance of ships' compasses by 
proximity of magnetic rocks under water at 
depths below the ship's bottom more than 
amply safe for the deepest ships. 


April 28, 1891. 




A Lecture delivered in the City Hal!, Glasgow, on 
Thursday, November II, 1875, under the Auspices 
of the Glasgow Science Lectures Association. 


Evening Lecture to the British Association at the 
Southampton Meeting, Friday, August 2$, 1882. 


Extracts from a Lecture on " The Tides" given to 

the Glasgou 1 Science Lectures Association, not 
hitherto published, and now included as explaining 
in greater detail certain paragraphs of the preced- 
ing Lecture. 


Abstract of a paper read at the />/>/*// (1878) meeting 
of the British Association. 



Abstract of paper by Captain Evans, R.N., F.K.S., 
and Sir William Thomson, LL.D., F.R.S., read 
in Section E of the Dublin (1878) meeting of the 
British Association. 


Circular issued by Sir William Thomson in Decem- 
ber, 1867, to the members of the Committee, ap- 
pointed, on his suggestion, by the British Association 
in 1867 "For the Purpose of Promoting the Ex- 
tension, Improvement, and Harmonic Analysis of 
r fidal Observations" 


Thomson and Taif s " Natural Philosophy," 804 



Taken from " Good Words ; " and United Service 
Institution Lectures, 1878 and 1880. 



Being extract from United Service Institution Lecture, 




Being extract from United Service Institution Lecture, 
1878 ; with, additions of date 1890. 


Being an account by Captain Creak, R.N., F. /v. S. , 
of observations made subsequently to those described 
on pp. 255 266. 


WIRE 337 

Paper communicated to the Society of Telegraph 
Engineers, Apr^l 22, 1874 





Extracts from paper read, and illustrated by apparatus 
exhibited, before United Service Institution, 
February 4, 1878. 


Paper read at the Naval and Marine Exhibition, 
Glasgow, Febrttary n, 1881. 





Address delivered before the Royal Society of Edin- 
burgh, December 18, 1865. 

CABLES OF 1858 AND 1865 413 



Lecture delivered at tJie Conversazione of the Institu- 
tion of Mechanical Engineers in the Science and 
Art Muscnin, Edinburgh, on Wednesday evening, 
yd August, 1887. 

INDEX 507 




popular ^cdurcs anb 


[A Lecture delivered in the City Hall, Glasgow, on 77mrsday, 
November nth, 1875 ; under the Auspices of the Glasgow 
Science Lect tires Association.] 

I. NAVIGATION, in the technical sense of the 
word, means the art of finding a ship's place at 
sea, and of directing her course for the purpose 
of reaching any desired place. The art of keeping 
a ship afloat, and managing her so as to follow 
the course traced out for her, belongs rather to 
what is technicaly called Seamanship than to 
Navigation ; still the two great branches of the 
sailor's art must always go hand in hand : all the 
great navigators have been admirable for their 
seamanship ; and every true seaman tries, as far as 


his circumstances permit, to be a navigator also. 
I have often admired the zeal with which even 
untaught sailors con over a chart when they get 
access to one, and the aptitude which they display 
for the scientific use of it. It is a common saying 
that sailors are stupid ; but I thoroughly and 
heartily repudiate it, not from any sentimental 
fancy, but from practical experience. No other 
class of artizans is more intelligent ; and, more- 
over, sailors' wits are kept sharp by the ever 
nearness of difficulties and dangers to be met by 
ready and quick action. The technical division 
between navigation and seamanship, if pushed so 
far as to leave one class of officers chiefly or wholly 
responsible for navigation and another for seaman- 
ship, would not tend to excellence or ski! fulness 
in either department. The subject of the present 
lecture is, however, Navigation in its technically 
restricted sense. 

2. To find a ship's place at sea is a practical 
application of Pure Geometry and Astronomy. It 
is on this piece of practical mathematics that I am 
now to speak to you. 


Four modes are used, separately or jointly, for 
finding the place of a ship at sea. 

I. PILOTAGE. Navigation in the neighbourhood 
of land. The means of finding the ship's place in 
pilotage are chiefly by sight of terrestrial objects, 
as headlands, lighthouses, landmarks, or hills, and 
other objects of known appearance, and by feeling 
the bottom by " hand-lead soundings." 

celestial objects sun, moon, planets, stars. 

Distance and direction travelled from a previously 
known position. 

IV. DEEP-SEA SOUNDINGS. Depth of water and 
character of bottom. 

3. The instruments and other aids used are : 
For tJie first mode. The sextant, the azimuth 
compass, station pointer, and other mathematical 
drawing instruments, charts, books of sailing 

For the second. The sextant, the chronometer, 
the Nautical Almanac, a book of mathematical 
tables, and mathematical drawing instruments. 

B 2 


For the third. A Massey's log (or instead of 
Massey's log, the old log-ship and glasses), the 
ordinary mariner's compass, a traverse table, 
mathematical drawing instruments, and a common 
clock or watch. 

For the fourth. The lead [with improvements 
described in 37 below], the instruments used for 
the third mode, arid a chart. 

I shall first briefly describe the instruments, 
beginning with the sextant. 

4. THE SEXTANT. The sextant is an admirably 
devised instrument, invented by Sir Isaac Newton 
(and first made by Hadley), for measuring, on 
board ship, the angle between any two visible 
objects. The general principle of the instrument 
is this : One object, A, is looked at directly, the 
other, B, by two reflections first, from a silvered 
mirror, and next from a piece of unsilvered plate- 
glass, in the manner illustrated in the drawing 
before you. The second of these mirrors is fixed 
on the framework. The first mirror, which is 
movable round an axis, is turned by the observer 
until the doubly reflected image of B is seen, like 


Pepper's ghost, in the transparent plate-glass 
coincidently with A seen through the same. From 
the law of reflection, that the incident and reflected 
rays make equal angles with the mirror, it is clear 
that when the silvered mirror is turned through 

FIG. i. Sextant. 

any angle, the ray reflected from it turns through 
twice as large an angle, and after its second re- 
flection (as the second mirror is fixed) it turns 
through still the same angle, that is to say, 
through twice the angle turned by the silvered 
mirror. The angles through which the silvered 


mirror is turned in the use of the sextant are 
measured by very fine divisions on an arc forming 
a sixth of the circumference of a circle, whence 
the instrument derives its name of sextant. 

5. Imagine now that I am standing on the 
ship and looking directly at the horizon. What 
do you mean by the horizon at sea ? It is the 
bounding line of sea and sky. It is a real 
line on the sea. When you look from the deck 
of a ship at the sea, you are looking down. 
Look as far as you can along the sea, and you 
are still looking somewhat downwards. The angle 
at which you must look down from the true level 
to see the line of the horizon is called the dip 
of the horizon. Looking then at the horizon, and 
turning the silvered mirror about with my left 
hand, I bring the ghostly image of the sun down 
till its lower edge touches the sea-horizon. I then 
look at the divided circle of the instrument, read 
off the number, and I have the angle through 
which I have had to turn the silvered mirror to 
bring down the image of the sun from the direction 
in which I had to look to see the sun directly, to 


the direction in which I must look to see the sea- 
horizon. This gives me what is called the apparent 
altitude of the sun. 

The framework of the instrument used in old 
times to be made of ebony, and the divided arc 
of ivory inlaid in it, as in one of the instruments 
before you. In the best modern sextants the 
framework is a light structure of brass, and the 
graduated arc is of silver, or of platinum, or of 
gold, inlaid in it. It is of silver in this other instru- 
ment before you (one of Troughton and Simms'). 

6. Now as to the divisions of the circular scale, 
I must tell you that, for the purpose of the 
measurement of angles, the complete circumference 
of a circle is divided into three hundred and 
sixty equal parts called degrees, so that a quarter 
round is measured by ninety degrees. The sixtieth 
part of a degree is called a minute of arc or of 
angle, and the sixtieth part of a minute is called 
a second of arc or of angle. The ambiguity of 
the names minute and second, sometimes used for 
angles, and more often, as you well know, for the 
reckoning of time, is perniciously troublesome in 


practice, and sometimes, though rarely, leads 
to temporary error through inadvertence on the 
part even of a careful and skilled navigator. It 
will torment us repeatedly in the course of the 
present lecture. 

7. As the sextant is used for the measurement 
of angles, the doubles of those turned through 
by the movable arm, its arc of sixty degrees is 
divided into 120 equal parts, and each of these 
parts is divided into three equal subdivisions. 
Thus, the subdivision which is actually 10' of arc 
measures 20' turned through by the reflected ray. 
The main divisions are numbered by fives from 
o to 1 20, and, being actually half degrees of arc, 
measure whole degrees turned through by the ray. 
When the minutest accuracy is aimed at the scale 
is read by aid of a vernier attached to the movable 
arm ; but in cases which frequently occur, where an 
error of four or five minutes of angle is of no moment, 
the reading is more easily taken directly by a single 
division marked on the movable arm. This single 
division is the zero line of the vernier, as illustrated 
by the drawing before you. The fractions of a sub- 


division are read off on the scale of the vernier, when 
they cannot be estimated directly with sufficient 
accuracy and readiness. A small magnifying lens is 
generally used in reading the scale with or without 
the vernier. 

8. Take now the instrument in your hand, and 
look at a distant object, A, through the unsilvered 
plate-glass, and turn the silvered mirror till the 
ghost of the same object A, seen by the double 
reflection, coincides precisely with the object itself 
seen directly. Then read, on the graduated scale, 
the number corresponding to the position of the 
marker carried by the turning arm. Suppose the 
reading to be 5'^. This is what is called the index 
error of the instrument. Now take the instrument 
in your hand again, and turn the arm carrying the 
silvered mirror round till the ghost of one object, B, 
seems coincident with the substance of another, 
A, seen through the unsilvered glass. Look at the 
scale again and take the reading, say 117 8': 
subtract the index error from this and you find 
1 17 2'f, which is the angle between A and B as 
seen from your actual position. 


9. A small telescope attached to the framework 
is generally used for magnifying the object and 
the ghost, which are both seen through it simul- 
taneously. It is removable, and it is often more 
convenient to do without it when the most minute 
accuracy is not required. It is not shown in the 
drawing before you. The only other optical adjuncts, 
besides the telescope and the magnifying lens for 
reading the scale, are two sets of coloured glasses, 
which may be placed in the way of rays coming 
from the silvered mirror to be reflected at the 
unsilvered glass, and of rays coming direct through 
the unsilvered glass. They are not shown in the 
drawing, but they are essential for observation of 
the sun. In moderately clear weather, and when 
the sun is at any considerable height above the 
horizon, even his ghostly image, by the second 
reflection at the unsilvered glass, is of dazzling 
brilliance, unless abated by one or more of the 
coloured glasses ; and when the sun is bright, but 
not very high above the horizon, the sea itself at 
the boundary between sea and sky under the sun 
is often too dazzling to be looked at in its un- 

NA VI G A TION. 1 1 

diminished brilliance ; then the coloured glasses in 
front of the unsilvered mirror must be put in 
requisition. Lastly, I must not omit to tell you 
that a portion of the glass which I have been 
speaking of as the unsilvered glass, or unsilvered 
mirror, is actually silvered ; but this portion is 
advantageously put out of the way (by means 
of a sliding piece and screw) in almost all 
ordinary uses of the instrument. It is useful for 
star observations when the ghostly image in the 
unsilvered part of the glass is too faint. 

10. THE AZIMUTH COMPASS. Before describ- 
ing the azimuth compass, I must tell you what an 
azimuth is. It is simply a horizontal angle. The 
azimuth of one object relatively to another, as 
you see the two from any particular place, is the 
angle between the two horizontal lines verti- 
cally under the directions in which you see the two 
objects. In navigation, azimuths, or " bearings," as 
they are commonly called by sailors, are generally 
measured from the true north, or from the magnetic 
north, point of the horizon. 

11. The true north is found, whether at sea or on 


shore, by observation of the heavenly bodies. Look 
at the stars, hour after hour, on a clear night, you 
will see them all seeming to turn round one point 
in the sky. That pivot point of the sky is called 
the north celestial pole. You understand that you 
are in the northern hemisphere. Any one south of 
the equator observing the stars similarly, would 
perceive in the southern sky another point, the 
south celestial pole, round which the stars there 
would seem to turn. 

12. The north and south terrestrial poles are 
those points on the earth's surface where the north 
celestial pole and the south celestial pole are exactly 
overhead, that is to say, they are the two points 
of the earth's surface whose verticals are precisely 
parallel to the axis of the earth's rotation. It is by 
finding the pivot point of the stars vertically over 
his head, that Captain Nares will recognise the 
north pole when he comes to it. 

13. There is no distinctly visible star exactly at 
the north celestial pole ; but there is one star of the 
second magnitude which nowadays is at a dis- 
tance of i 2 1' from it. This star is therefore now 


called Polaris, or the pole star, and it will probably, 
if there is continuity of men and books upon the 
earth, still have the same name twelve thousand 
years hence, when it will be 47-| from the north 
celestial pole. 


FIG. 2. Illustrating Precession. 

In the dawn of human history the earth's axis 
pointed to a star not enduringly named till nearly 
2000 years later, when the pole had moved about 
10 or 1 1 from it, and it was called by the Greeks 
a Draconis. 

14. The diagram before you, Fig. 2, shows how 


the north celestial pole has moved among the stars 
for thousands of years, and may be expected to 
move for hundreds of thousands of years to come. 
It represents a small circle among the stars on which 
the earth's celestial pole travels at the rate of once 
round in 25,868 years, or at the rate of i of great 
circle per 180 years. The diameter of this circle 
is about 47 (more nearly 4655'), and its centre 
is in the direction perpendicular to the plane of 
the earth's orbit round the sun. 1 To understand 
this motion, and its effect on the line of the 
equinoxes, as the line of intersection of the 
earth's equator and the ecliptic is called, look at 
the model before you which shows the rotation 
of the earth round an axis constantly changing 
position in space. The line of the equinoxes 
travels once completely round the ecliptic in 
25,868 years, or at the rate of i per 71-85 years 
in the direction contrary to the earth's rotation. 
This motion is called the precession of the 

1 Or is what is called the " pole of the ecliptic," the ecliptic being 
a name given by the Greeks to the plane of the earth's orbit, because 
the moon must be nearly, if not exactly, in this plane to produce or 
experience an eclipse. 


equinoxes. If the earth revolved under guidance 
of a mechanism such as this model, the circum- 
ference of its rolling pivot-shaft would be 5! feet 
and that of the fixed ring or hoop on which it 
rolls, 52,000,000 feet. 

FIG. 3. Precessional Model. 

15. Our astronomical knowledge of the pre- 
cession of the equinoxes has given a most 
interesting and marvellous assistance to historians 
in estimating the date of the pyramid-building 
of Egypt. In six of the pyramids of Gizeh and 


two of the pyramids of Abooseer are found 
tunnels pointing in a certain direction towards 
the heavens. The directions of these tunnels are 
from 26 to 28 above the horizon, and in true 
north azimuth. They are from 4 to 2 under 
the north celestial pole (the latitude of the place 
being 30). It has been conjectured, with con- 
siderable probability, that they were designedly 
made in such directions as to let the then' pole 
star be seen through them at its lower transit. 
There was then no star so near the pole as our 
present Polaris. The nearest was a Draconis, 
which, from 3564 B.C. to 2124 B.C., had the pole 
within 4 of it, at distances varying as shown in 
the annexed table : 


Distance of j 
u Draconis 


B C. 

from pole. 
















2 4 84 





I '02 









The building of the pyramids might therefore 
have been at any time from 2480 B.C. to 2120 B.C., 
or at any time from 3560 B.C. to 3200 B.C., to 
suit the astronomical hypothesis. It was supposed 
to be about 2100 B.C. when Sir John Herschel 
first took up the question at the request of Col. 
Howard Vyse. Now, from independent historical 
evidence, 1 the date 3200 is the most probable. 
The astronomical hypothesis cannot decide be- 
tween these two dates, but if it were granted, it 
would show that either of them is more probable 
than any date between 3200 B.C. and 2480 B.C. 

1 6. The point on the horizon under the north 
celestial pole is called the true North ; the true 

1 I am informed by my late colleague, Professor Lushington, that 
"the whole chronology of early Egyptian times is perplexingly ob- 
scure ; probably a dozen different systems have been built on equally 
stable foundations. The latest attempt known to me to establish a 
real basis is given in a little treatise by Diimichen, which is, I 
believe, in the University Library ; it rests upon a comparison of the 
fixed and vague year, found coupled with the name of a king which 
is read as Bicheris, the sixth name in Manetho's list of the fourth 
dynasty (the great pyramid dynasty). It would bring his time to 
about 3000 B.C., and the pyramids from 100 to 200 years earlier. 
It is found on the back of a huge papyrus just published at Leipzig 
by G. Ebers in facsimile, a most important work, being the largest 
and clearest written papyrus known, the contents chiefly medical.'* 



East and West, and the true South, are the 
points in the directions at right angles to it, and 
in the direction opposite to it, each on the horizon. 
The four right angles between these four cardinal 
points, as they are called, are, in nautical usage, 
divided each into eight equal parts, and the 
successive points of division, from N. by E. round 
to N. again, are called N. by E., N.N.E., N.E. by 
N., N.E., N.E. by E., E.N.E., E. by N, E. ; E. 
by S., and so on. A part of the early training 
of the young navigator used to be to rattle over 
these designations as fast as his youthful tongue 
could utter them ; and this exercise was some- 
what comically called "boxing the compass." 
The successive angular spaces from point to 
point of the compass are generally divided into 
four equal parts, and the corresponding divisions 
are read off by quarters, halves, and three- 
quarters ; for example, thus N.JE., N.|E., N.f E., 
and so on. 

17. The term "point" is habitually used without 
any inconvenient ambiguity, sometimes to denote 
one of the thirty-two directions corresponding to 


the points of division, and sometimes any angular 
space that is equal to the space from one of the 
thirty-two points to the next on either side of 

FIG. 4. Compass Card. 

it. The terms quarter-point and half-point are 
sometimes applied to the subdividing marks, but 
more often to designate the angular spaces between 
them. From what I have told you already, you 

C 2 


now see that the angle from point to point of 
the compass is the eighth part of 90, that is to 
say, i iJ. This is just two per cent, less than 
one-fifth of the radian. 1 Hence nearly enough 
for most practical purposes, you may reckon that 
an error of one point in steering will lead you 
wrong one mile in five. More precisely reckoned, 
an error of a quarter-point will lead you wrong 
one mile in twenty and a half. 

1 8. The magnetic north and south points are 
the points of the horizon marked by the direction 
in which a thin straight magnetised steel needle 
rests when balanced on a point, or hung by a 
fine fibre, so as to be very free to turn round 
horizontally. A magnet of any shape or kind, 
for example, a bar or horse-shoe of magnetised 
steel, or a lump of loadstone, or even an electro- 
magnet, if somehow supported by its centre of 
gravity, but free to turn round it, will not rest 
indifferently in all positions, but balances only 
when a certain line of it, which is called its 

1 The " radian " is an angle whose arc is equal to the radius 
it is 57'3, or thereabouts. 


magnetic axis, is in a particular direction de- 
pending on the particular locality in which the 
experiment is made. This direction is actually 
shown by the " dipping needle." The ordinary 
horizontal needle tends to dip into the same 
direction, but is prevented by a counterpoise 
adjusted to keep it horizontal. The dipping 
needle is vertical at the two magnetic poles, and 
there the horizontal needle shows no direction. 
Early Arctic navigators imagined the magnetic 
virtue to be impaired by cold, when they found 
their compasses becoming sluggish as they ap- 
proached the north magnetic pole ; but the 
dipping needle disproves this idea by vibrating 
actually with greater energy, rather than with less, 
in polar regions. The charts (Figs. 5 and 6) before 
you explain sufficiently how the magnetic north 
and south line lies in any part of the world. 

19. The lines on these diagrams show what 
Faraday would have called the lines of horizontal 
magnetic force. They are sometimes called 
magnetic meridians. All these curved magnetic 
north and south lines pass through two points 


a north magnetic pole and a south magnetic 
pole. The north magnetic direction in any one 
of them is that which leads you to the north 
magnetic pole. You see that in the northern 


I-'IG. 5. Magnetic Chart: Northern Hemisphere. 

polar region, between the true north pole and 
the magnetic north pole, the north magnetic 
direction leads obliquely, or directly, southward ; 
and, again, in the region between the true south 


pole and the magnetic south pole, the south 
magnetic direction leads obliquely, or directly, 
northward. In all places of the world, except 
these Arctic and Antarctic regions between the 

FIG. 6. Magnetic Chart : Southern Hemisphere. 

magnetic and the true poles, the magnetic north 
and magnetic south directions are northward and 
southward ; but agree exactly with the true 
north and south directions only on certain lines 


of the earth's surface, as the reader will readily 
see and understand by looking at the annexed 
magnetic charts, Figs. 5 and 6 (pp. 22 and 23). 
Observation shows that nowadays the lines of 
horizontal magnetic force are as represented on 
the diagrams before you. But a comparison with 
observations made within the last 300 years shows 
us that the magnetic poles and lines of force are 
changing. Three hundred years ago (1576), in 
London, the compass pointed to the east of 
north. Two hundred and seventeen years ago 
O^SQ)) the compass pointed due north there. 
After that, for 164 years, it showed an increasing 
westerly direction, till in 1823 it pointed 24' 30' 
to the west of north, and began to come back 
towards the north. Now its deviation in London 
is only 20 30' west, and it is decreasing about 
6' annually. Here, at Glasgow, the deviation is 
at present about 24 west. 

20, The dip at London is now about 67 40', 
at Glasgow 71, and for the British Islands it is 
at present decreasing at about 2*69' annually. It 
is ascertained to have been decreasing during 


the last 20 years, and no doubt it has been 
decreasing during the 217 years which have 
elapsed since the needle pointed due north. 

21. The fact brought out is, that the whole 
system of terrestrial magnetism, with its poles 
and lines of force, is travelling round the earth's 
axis at the rate of once round, relatively to the 
earth, in 960 years, backwards or the way of 
the sun ; or, which amounts to the same, the 
system of terrestrial magnetism lags behind the 
earth's rotation at the rate of one turn less per 
960 years. The north magnetic pole is about 
20 from the true north pole. In 1659, the north 
magnetic pole was between London and the true 
north pole, and since that time it has travelled 
82 westwards in a circle round the true pole, so 
that it is now in about 82 of west longitude, 
and still 20 from the true north pole. 

In the year 2139, it may be expected to be 
again due north of London, but on the far side of 
the true north pole in longitude 180, and so on. 

AZIMUTH COMPASS. The mariner's compass is 


an instrument adapted for showing, in a manner 
most convenient to the mariner, the azimuth of 
the ship's length relatively to the magnetic north 
and south line. It consists of a circle of card- 
board, or of mica coated with paper, marked on 
its upper side with the points of the compass, or 
degrees, or both points and degrees, and carrying 
two or four parallel bars of magnetised steel 
attached to it below, and an inverted cup of 
sapphire or ruby, or other hard material, attached 
to it over a hole in its centre. It is supported 
by the crown of the cup resting on a hard metal 
point standing up from the bottom of a hollow 
case called the compass bowl. The compass bowl 
is covered with glass to protect the card against 
wind and weather, and the bowl is hung on 
gimbals in a binnacle attached to the deck, and 
bearing convenient appliances for placing lamps 
to illuminate the card by night. The cheapest 
and roughest instrument made according to this 
description provided the bearing cup is of hard 
enough material and properly shaped, and provided 
the bearing point is kept sufficiently fine by 


occasional regrinding, or by the substitution of a 
fresh point for one worn blunt by sea use is 
accurate enough for the most refined navigation, 
and is perfectly convenient for use at sea, on 
board of any ordinary wooden sailing ship, large 
or small, in all ordinary circumstances of waves 
and weather. 

23. If it were my lot to speak to you for a 
whole evening on the subject of the mariner's 
compass, I would have to tell you of the qualities 
which the instrument must possess to render it 
suitable for use in all ships, and all seas, and all 
weathers, and of the correctors which must be 
applied to it if it is to point correctly in iron 
ships. To-night, I cannot for want of time. 
[See articles on the compass below.] The azimuth 
compass, for use at sea, is an ordinary mariner's 
compass, with the addition of a simple appliance for 
measuring the azimuths of celestial or terrestrial 
objects on its card with great accuracy. 

24. GLOBES AND CHARTS. A celestial and ter- 
restrial globe ought both to be found in every 
school of every class. In navigation schools, much 


of the difficulty in understanding the methods of 
spherical astronomy taught there for subsequent 
daily use at sea, would be smoothed down by aid of 
either the celestial or the terrestrial globe or both. 
The mystery of great circle sailing is done away 
with by merely looking at a terrestrial globe ; and 
in actual practice at sea, a terrestrial globe would 
be exceedingly useful in laying out great circle 
courses, and planning the courses to be actually 
sailed over, and for approximate measurements of 
great distances on the earth's surface, instead of 
laboriously (and sometimes with useless exactness) 
working out these questions by a blind use of 
logarithms. The celestial globe would be exceed- 
ingly useful at sea for facilitating the identification 
of stars to be used for finding the ship's position by 
altitudes, or correcting the compass by azimuths. 
A blackened globe, upon which circles can be 
drawn in chalk, is also useful at sea for approxi- 
mate solutions of some problems which occasionally 
occur, and is indispensable in a navigation school 
whether on shore or on board ship, for the in- 
struction of young officers. Still the main work 


of navigation must be laid down on charts. 
Though useful auxiliary drawings may be done on 
the round surface of a blackened globe, you cannot 
draw a straight line on a globe, and for accurate 
drawing with existing mathematical instruments, a 
flat surface is necessary. 

25. The various kinds of projections to be found 
in different maps and atlases would take too long 
to describe, but except for polar regions, the only 
one of them used in navigation is that very 
celebrated one called Mercator's projection, and I 
shall therefore limit myself to describing it to you 
this evening. It has the great advantage, that it 
shows every island, every cape, every bay, every 
coast line, if not too large, sensibly in true shape. 
Every course, every direction, at any point of the 
earth's surface, is shown precisely in its true 
direction on Mercator's projection. Imagine a skin 
of paper to coat this globe before you as the skin 
of an orange coats an orange. Imagine a hole 
made at the north pole, and another at the south 
pole, and the skin to be stretched out without 
altering the length from equator to either pole. Or 


suppose you were to cut the skin into countless 
liths, and then cutting it open across one point of 
the equator, lay it flat and fill up the spaces 
between the liths : then you have a plane drawing 
or chart of the earth's surface such as the ac- 
companying diagram, Fig. 7, shows. You have 





20 20 

FIG. 7. Plane Chart. 

stretched the polar regions in longitude without 
altering them in the north and south direction. 
Stretch them now polewards north and south to 
the same proportionate extent as you have already 
stretched them in longitude. By doing so you 
put the north and south pole away to an infinite 
distance and lose the polar regions, but you thus 


get a very convenient chart for the middle and 
tropical regions, which is called Mercator's pro- 
jection. It is illustrated in the annexed diagram, 
Fig. 8. Contrast the shapes of Greenland as 
shown on these two charts, Figs. 7 and 8, with 


40 20 20 40 60 

FlG. 8. Chart on Mercator's Projection. 

one another, and with that shown on the magnetic 
chart of the northern hemisphere, Fig. 5 (p. 22\ 
which is more nearly the true shape than either. 

A " great circle " of the earth's surface is a circle 
whose plane passes through the earth's centre. 
Any diameter of the great circle measured along 


the surface is 180; and the shortest line on the 
surface from any one point to any other, must 
clearly lie along a great circle. Look at your 
terrestrial globe to illustrate this. The Mercator 
chart before you, extending from latitude 40 to 
latitude 80, shows what great circles look like on 
Mercator's projection. One of the lines is a great 
circle from Cape Farewell to a point in longitude 
70 E., latitude 50 N. The other is a great circle 
from Valentia to Trinity Bay, Newfoundland, along 
which the original Atlantic cables were laid. 

The oval curves on the Mercator's projection of 
56, Fig. 14 below, represent what are in reality two 
circles on the earth's surface, drawn for the purpose 
of illustrating Sumner's method, to be explained 
later. They are what are technically called " small 
circles," their diameters being respectively 100 and 
80, and their centres inlat. 10 N. 

26. STATION POINTER. The station pointer 
consists of three rulers turning in one plane round 
a common centre, with their edges so set as to 
radiate from this centre, and with a graduated arc 
showing the inclinations of the edges one to 


another. The common hinge or joint is open in 
its centre ; the actual central point from which the 
three edges of the three rulers radiate is marked 
by a pointer attached to one of the three limbs. 

27. THE CHRONOMETER. For the second mode 
of navigation, the chronometer is the only other 
instrument I have to mention. The object of the 
chronometer is to show Greenwich time all over the 
world. It is merely a watch adapted to go with 
the greatest possible accuracy. The main feature 
of the chronometer, besides very fine finish in all its 
parts, and an escapement movement of peculiar 
excellence, is that the vibrating balance-wheel is 
" compensated " for variation of temperature. An 
ordinary balance-wheel, with continuous rim of 
one metal, vibrates more slowly at high than at 
low temperatures, because the hair-spring has less 
of elastic stiffness, and because the balance-wheel 
is larger, at higher temperatures ; but a small part 
only of the whole difference in time-keeping de- 
pends on the last-mentioned cause. About twelve- 
thirteenths of it is due to the diminished elastic 
stiffness of the hair-spring. In the compensated 



balance-wheel, the rim is composed of two metals, 
the outer part brass, the inner part steel, and it 
is cut into two halves, which are nearly semi- 
circular, and are supported by one end attached 
to one end of a stout diameter of the wheel, Fig. 9. 
Weights are attached to the two semicircles in 

FIG. 9. Chronometer Balance Wheel. 

proper positions, to produce, as nearly as possible^ 
the desired equality of period of vibration for 
different temperatures, according to the following 
principle : When the temperature is augmented, 
the two halves of the rim, supported as they are on 
two ends of one diameter, curve inwards from their 
outer parts being brass (more expansible), and the 


inner parts steel (less expansible), and thus carry 
the attached weights inwards. The whole vibrating 
mass, composed of axle, diameter, rims, and at- 
tached weights, has thus less moment of inertia, 
and so, with the less elastic stiffness of the hair- 
spring, the balance-wheel vibrates with the same 

This mode of compensating for temperature was 
invented about one hundred years ago by Thomas 
Earnshaw, to whom is also due the excellent form 
of escapement now universally used in the marine 

28. The first chronometer used for determining 
the longitude was invented by John Harrison, and 
completed by him in a life-work of fifty years. 
The origin of this first marine chronometer pre- 
sents a most interesting chapter in the history of 
inventions. Sir Isaac Newton pointed out the 
great importance of an accurate chronometer at 
sea, for determining the longitude. On the I ith of 
June, 1714, the House of Commons appointed a 
Committee, of whom he was one, to consider the 
question of encouragement for the invention cf 

D 2 


means for finding the longitude. This Committee 
gave in a report explaining different means by 
which the longitude could be found, and recom- 
mending encouragement for the construction of 
chronometers as likely to lead to a better solution 
of this important problem of navigation than any 
other that had been or could be devised. In 
consequence of this report, an Act of Parliament 
was passed offering prizes of i,ooo/., I5,ooo/., and 
2O,ooo/., for the discovery of a method for deter- 
mining the longitude within 60, 40, and 30 miles 
respectively : " one moiety or half part of such 
" reward or sum shall be due and paid when 
" the said commissioners, or the major part of 
" them, do agree that any such method extends to 
11 the security of ships within 80 geographical 
" miles of the shores which are places of the 
" greatest danger, and the other moiety or half 
" part when a ship, by the appointment of the said 
" commissioners, or the major part of them, shall 
" thereby sail over the ocean from Great Britain to 
" any such part in the West Indies as those com- 
" missioners, or the major part of them, shall choose 


" or nominate for the experiment, without losing 
" their longitude beyond the limits before 
" mentioned." l 

After first completing a chronometer in 1736, 
Harrison offered a chronometer to the commis- 
sioners for this prize, which, tried " in a voyage to 
Jamaica in 1761-62, was found to determine the 
longitude within 18 miles ; he therefore claimed 
the reward of 2O,ooo/., which, after a delay caused 
by another voyage to Jamaica, and further trials, 
was awarded to him in 1765 io,ooo/. to be paid 
on Harrison's explaining the principle of con- 
struction of his chronometer, and io,ooo/. whenever 
it was ascertained that the instrument could be 
made by others. The success of Harrison's 
chronometer is owing to his application of the 
compensation curb to the balance-wheel, and on the 
same principle he invented the gridiron pendulum^ 
for clocks. These, along with his other inventions, 
the going fusee, and the remontoir escapement, 
were considered to be the most remarkable im- 
provements in the manufacture of watches of the 

1 Extract from Act of Parliament passed in 1714. 


last century. Harrison died in Red Lion Square, 
London, in I/76." 1 

Harrison's compensation curb, here referred to, 
was a contrivance in which the bending of a com- 
pound bar of brass and steel soldered together was 
applied to shorten the vibrating portion of the 
hair-spring of the watch when the temperature 
rises, and elongate it again when the temperature 
falls. The very different method of compensation 
subsequently invented by Earnshaw was no doubt 
much superior, but Harrison's curb must always be 
interesting as the first successful method for com- 
pensating the temperature error of a watch, and 
the first usefully applied to determine the longitude 
at sea. 

29. The most important improvement in marine 
chronometry since the time of Earnshaw has been 
made by Mr. Hartnup, Astronomer to the Marine 
Committee of the Mersey Docks and Harbour 
Board of Liverpool. It had been long known that 
the simple compensation balance, whether of 
Harrison or Earnshaw, however perfectly executed 

1 Chambcrs's Encyclopaedia, Art. "Harrison." 


in workmanship, and however carefully adjusted 
by trial, does not give equable time-keeping at all 
temperatures through wide natural ranges. It had 
been sought to remedy this defect by the appli- 
cation of secondary compensation on various 
ingenious plans, but with no practical success. 
Thus the best chronometers of the best makers 
in modern times are practically perfect only 
within a range of 5 or 10 Fahrenheit on each 
side of a certain temperature, infinitely near to 
which the compensation is perfect in the individual 

The temperature for which the compensation is 
perfect, and the amount of deviation from per- 
fection at temperatures differing from it are 
different in different chronometers. Mr. Hartnup 
finds that at the temperature for which the com- 
pensation is perfect, the chronometer goes faster 
than at any other temperature, and that the rate 
at any other temperature is calculated with 
marvellous accuracy (if the chronometer be a good 
one) by subtracting from the rate at that critical 
temperature the number obtained by multiplying 


the square of the difference of temperature by 
a certain constant co-efficient This constant co- 
efficient and the temperature of maximum rate 
remain the same for the same chronometer until 
it is cleaned or repaired, or until it requires to be 
cleaned or repaired. Thus, for example, a certain 
chronometer, " J. Bassnett & Son, No. 713," after 
being rated by Mr. Hartnup, was put on board the 
ship Tenasserim, in Liverpool, December, 1873, for 
a voyage to Calcutta. The result of Mr. Hartnup's 
rating and the application of his method showed 
that this chronometer had its maximum rate at 
temperature 70 Fahrenheit, and that the difference 
of rates at any other temperature, reckoned in 
seconds or fractions of a second per day, was to 
be calculated by multiplying the square of the 
difference of temperature from 70 into '0034 sec. 
Thus at 80 or 60, the chronometer would go 
slower than at 70 by "34 of a second per 
day ; at 90 or at 50 it would go slower than 
at 70 by 1*36 seconds per day ; and so on for 
other temperatures. 

The ship sailed from Liverpool on the 2ist of 


January, 1874, and on her voyage to Calcutta the 
chronometer was subjected to variations of temper- 
ature ranging from 50 to 90. The chronometer 
was tested by the Calcutta time-gun on the 26th of 
May. The time reckoned by it, with correction 
for temperature on Hartnup's plan, was found 
wrong by 8J seconds. Another chronometer, 
similarly corrected by Mr. Hartnup's method, and 
from his rating, gave an error of only 3^ seconds. 
The difference between the reckonings of the two 
chronometers was thus only 5 seconds, and the 
error in reckoning by taking the mean between 
them only 6 seconds. This corresponds to an 
error of only a mile and a half in estimating the 
ship's place in tropical regions. The reckonings of 
Greenwich time from the two chronometers, 
according to the ordinary method, differed actually 
by 4 minutes 35 seconds, corresponding to 68 J 
geographical miles of error for the ship's place. 

From Mr. Hartnup's investigations, it is 
obvious that one important point for a good 
chronometer is, that the temperature of maximum 
rate should be as nearly as may be the mean 


temperature at which it is to be used ; but the 
main quality required for good work is constancy 
in temperature of maximum rate, and in co- 
efficient for calculating rates at other temperatures. 

To facilitate the application of Hartnup's 
method at sea, a small thermometer, to be placed 
in the chronometer case, with a scale graduated 
not to degrees but to squares of numbers of 
degrees of difference from the temperature of 
maximum rate, would be a valuable adjunct to be 
supplied to every chronometer. The navigator in 
winding his chronometer daily, would look at this 
thermometer, and enter two or three figures in a 
properly prepared chronometer rate-and-reckoning- 
book. All that he would have to do, thus, to take 
full advantage of Hartnup's method, need not 
occupy more time than about as much as it takes 
him to wind his chronometer. 

AND DISTANCE RUN. The name log was origin- 
ally applied to a floating piece of wood, by the 
aid of which the speed of a ship through the 
water was determined. What is commonly called 


at sea the " Dutchman's log " is a very primitive 
method of measuring speed, in which a bottle is 
thrown overboard from the bow, and its times of 
passing two fixed marks, at a measured distance 
apart on the ship, are observed. But primitive 
as it is, it is more accurate than any other method 
which has ever been practised for low speeds 
and large ships. Suppose, for example, the marks 
to be 250 feet apart, and the times of the floater 
passing them to be 

ih. 1 7m. I2s. 
and ih. I7m. 48^5. 

The interval, therefore, was 36^ seconds. Hence 
the ship went 250 feet in 36 J seconds, and therefore 
was going at the rate of 1000 feet in 146 seconds. 
To find the rate in miles per hour, multiply the 
number of feet per second by 3600 and divide by 
6080. The result is 4-05. Therefore the ship was 
going at the rate of 4*05 miles per hour. This 
process would of course, be too troublesome for 
ordinary use, requiring as it does two accurate 
observers with watches having seconds hands, 
and an assistant. It would be found, however, 


exceedingly useful in some circumstances for 
speeds below six or seven knots. 

31. The following description of the LOG AND 
GLASSES in ordinary use is taken from Lieutenant 
Raper's excellent book on navigation. 1 

" THE LOG. The log consists of the log-ship 
and line. The log-ship is a thin wooden quadrant, 
of about five inches radius ; the circular edge is 
loaded with lead, to make it float upright, and 
at each end is a hole. The inner end of the 
log-line is fastened to a reel, the other is rove 
through the log-ship and knotted ; and a piece 
of about eight inches of the same line is spliced 
into it at this distance from the log-ship, having 
at the other end a peg of wood, or bone, which, 
when the log is hove, is pressed firmly into the 
unoccupied hole. 

"At 10 or 12 fathoms from the log-ship a bit 
of bunting rag is placed to mark off a sufficiency 
of line, called stray-line, to let the log go clear of 
the ship before the time is counted. 

1 The Practice of Navigation and Nautical Astronomy, by Lieut. 
Henry Raper, R.N. (tenth edition, 1870; original edition, 1840). 


" The log-line is divided into equal portions 
called knots, at each of which a bit of string, with 
the number of knots upon it, is put through the 

" The length of a knot depends on the number 
of seconds which the glasses measure, and is thus 
determined : 

" No. of ft. in I knot : No. of ft. I m. : : No. of sees, of the glass : 
3600 (No. of seconds in an hour). 

" The nautical mile being about 6080 feet, we 
have, for the glass of 30 seconds, the knot 
= (6080 x 3o)/36oo = 507 feet, or 50 feet 8 
inches ; for the glass of 28 seconds, the knot 
= (6080 X 28)/36oo = 47*3 inches, or 47 feet 
4 inches, and so for any other glass. 

"The log-line should be repeatedly examined, 
by comparing each knot with the distance between 
the nails, which are (or should be) placed on the 
deck for this purpose at the proper distance. The 
line should be wet whenever it is required thus 
to remeasure it, or to verify the marks. 

"As the manner of heaving the log must be 
learned at sea, it is only necessary to remark, for 


reference, that the line is to be faked in the 
hand, not coiled ; that the log-ship is to be thrown 
out well to leeward to clear the eddies near the 
wake, and in such a manner that it may enter the 
water perpendicularly, and not fall flat upon it ; 
and that before a heavy sea the line should be paid 
out rapidly when the stern is rising, not when the 
stern is falling ; as this motion slacks the line, the 
reel should be retarded. 

32. " Massey's Log. This instrument shows the 
distance actually gone by the ship through the 
water, by means of the revolutions of a fly, towed 
astern, which are registered on a dial plate. 
This log is highly approved in practice ; and 
it is much to be desired that the patentee could 
manufacture, at a moderate price, an instrument 
which affords a method, at once so simple and 
so accurate, of measuring a ship's way, and 
which could not fail to come into extensive, if 
not genera 1 , use. 

33. " The Ground Log. When the water is 
shoal, and the set of the tides or current much 
affected by the irregularity of the channel, or 


other causes ; and when, at the same time, either 
the ship is altogether out of sight of land, or 
the shore presents no distinct objects by which 
to fix her position, recourse may be had to the 
ground log. This is a small lead, with a line 
divided like the log-line, the lead remaining 
fixed at the bottom ; the line exhibits the effect 
of the combined motion of the ship through the 
water, and that of the water itself, or the current ; 
and therefore the course (by compass), and distance 
made good are obtained at once. 

34. "THE GLASSES. The long glass runs out 
in 3O S or in 28 s ; the short glass runs out in 
half the time of the long one. 

" When the ship goes more than five knots, the 
short glass is used, and the number of knots shown 
is doubled. 

"The sand-glasses should frequently be ex- 
amined by a seconds watch, as in damp weather 
they are often retarded, 1 and sometimes hang 
altogether. One end is stopped with a cork, which 

1 Why is the glass not hermetically sealed so that the sand put 
in dry may remain dry for ever ? (W. T.) 


is taken out to dry the sand, or to change its 

Lieutenant Raper's anticipation, published first 
in 1840, that the Massey log would come into 
extensive, if not general, use, has been amply 
verified. It is now to be found, I believe, on 
board of almost every British ship, not running 
at too great a speed for its use. It is the instru- 
ment chiefly trusted for finding distances run at sea, 
failing sights of sun or of stars ; and the old log-ship 
and glass, though capable of doing very good work 
in careful hands, has fallen, or is falling, into 
general disuse. The Massey log is kept con- 
tinually in tow when the ship is out of sight of 
land, except for a few minutes occasionally, when 
it is taken on board and its dial read off. Its 
reckoning of the distance run in different con- 
ditions of the sea and wind, in clear weather is 
checked by the ordinary astronomical observations. 
Then judging from the results, the navigator cor- 
rects its indications, if necessary, before using them 
to estimate the distance run in cloudy weather. 
All the different kinds of logs, which I have now 


explained, depend, you will perceive, upon a 
measurement of the distance actually run, in 
some particular interval of time, long or short. 

35. THE DEEP-SEA LEAD. The deep-sea lead 
is about 56 Ibs. in weight, with a hollow in its lower 
end, armed with stiff wax or tallow to bring up 
specimens of the bottom, and is attached to a 
rope of I \ in. circumference, and from 100 to 
200 fathoms in length. If the depth is to be 
found simply by the quantity of rope carried out 
by the lead before it reaches the bottom, the ship's 
way through the water must be as nearly as 
possible stopped if the depth is anything more 
than twenty fathoms. But by the introduction of 
a " Massey Sounding Fly " l a few feet above the 
lead, and in line between it and the rope, the 
distance travelled by the lead through the water 
may be measured with considerable accuracy, and 
thus soundings may be taken from a steamer going 
at full speed, even when the depth is as much as 

1 In the tenth edition of Raper's Navigation (1870) I find an 
amusing statement given on the authority of the "Survey of the 
River St. Lawrence," by Capt. Bayfiald, that "In depths exceeding 
100 fathoms, the fly is liable to be crushed." 



fifty or sixty fathoms. Suppose the ship is going 
at 12 knots, and it is important not to lose time 
by heaving to, or even by reducing speed ; the lead, 
with Massey fly and rope attached, is carried 
forward as far towards the bow as possible. Two or 
three coils of the rope are carried outside of the rig- 
ging, and several men, at different places along the 
ship's side, stand by, each with a coil or two of it 
in his hands. The foremost man casts the lead ; 
when the next man feels 'the rope beginning to pull 
he lets go, and so on. By the time the ship's stern 
has passed, the lead may have reached the bottom, 
or it may not have reached the bottom until a con- 
siderable distance astern of the ship. It is very 
hard work pulling in 1 50 or 200 fathoms of the thick 
deep-sea sounding rope, with 56 Ibs. at the end of 
it, when the ship is going at any such speed as 
12 knots through the water, even with twenty or 
thirty men employed to do it ; but a careful and 
judicious navigator will not spare his ship's com- 
pany. He will keep them sounding every hour or 
every half hour rather than run any unnecessary 
risk, and (if to lose no time is important) he will 


only reduce speed when he cannot, at full speed, 
take the soundings required for safety. 

36. I have shown elsewhere l that the labour of 
taking deep-sea soundings, whether for surveys of 
the ocean's bed, or for guidance in cable laying, 
or for ordinary navigation, may be immensely 
diminished, and the quickness, sureness, and 
accuracy of the operation much increased by the 
use of steel pianoforte-wire instead of hemp rope. 
You see before you a first rough attempt at an 
instrument for ordinary navigational sounding by 
pianoforte wire. I have tested its efficiency off 
the Island of Madeira, and off Cape Finisterre, and 
Cape Villano, at the south-west corner of the Bay 
of Biscay, and found it to work perfectly well. 
Even without the Massey fly, it gives a fairly 
approximate sounding in as great a depth as 1 50 
fathoms, when the ship is running at any speed not 
exceeding five or six knots, a result quite unattain- 
able by the ordinary deep-sea lead. There is no 
difficulty whatever in using it with a Massey fly 

1 See papers on "Deep- Sea Sounding" included in present 
volume ; also 37 below. 

E 2 


attached, although I have not yet tested it with 
this adjunct. With or without the Massey fly it 
can be hauled in quite easily by two men, though 
the ship is going at a speed of twelve knots. The 
whole watch in a large steamer is habitually em- 
ployed in hauling in the ordinary deep-sea lead, 
when soundings are taken with the ship going at 
full speed. 

[37. ADDITION OF AUGUST 4, 1887. The 
machine referred to in the preceding paragraph 
has, since this lecture was delivered, been developed 
and become a practical and useful aid to naviga- 
tion. The diagram (Fig. 10) shows the machine 
in the position for taking a cast. The steel wire 
is coiled on a V' sria P e d ring, A. This ring A can 
revolve independently of the spindle, or it may be 
clamped to the spindle by means of the plate BB. 
When the ring A is undamped from the spindle 
the sinker descends and the wire runs out. As 
soon as the sinker touches the bottom the wire 
slacks. The ring is then clamped to the spindle, 
which prevents any more wire running out, and 
winding in commences. The sinker is a hollow 


FIG. 10. Navigational Sounding Machine. 


tube, inside of which is placed 
the depth-recorder represented at 
Fig. n, for showing the depth to 
which the sinker goes. As the 
sinker descends the increased pres- 
sure forces the piston D up into an 
air-vessel, while the spiral spring 
pulls the piston back. The amount 
that the piston is forced up 
against the action of the spiral 
spring depends on the depth. The 
marker C is used for recording 
the depth. As the sinker goes 
down, the 'marker is pushed along 
the piston-rod. When the recorder 
is brought to the surface of the 
water, the piston comes back to 
its original position, but the marker 
remains at the place on the piston- 
rod to which it was pushed. The 
depth is read off by the position of 

FlG> ' 0613111 the cross wire f tlie mai ~ker on the 
scale of the piston-rod.] 



38. Sure and ready knowledge of the general 
appearance of the places visible from the ship's 
course is the first requisite in a pilot. It was 
probably the only kind of navigational skill, except 
taking soundings, possessed by the ancient Medi- 
terranean navigators, or by European navigators 
generally, until nine hundred years ago, when the 
mariner's compass first became known in Europe. 

When there are outlying dangers (as shoals and 
sunken rocks are technically called in navigation), 
the pilot must know familiarly their positions, with 
reference to visible objects on the shore, or on 
islands and rocks standing out above the water. 
Mere acquaintance with the general appearance of 
the visible objects no longer suffices, and the pilot, 
however unscholarly may have been his training, 
becomes of necessity a practical mathematician. 
The principle of clearing marks for dangers is of 
the purest geometry. A certain line is described 


or specified by aid of two objects seen in line 
or nearly so, or one over the other. The danger 
lies altogether on one side of this line ; or, it may 
be, a line so specified is a safe course between two 

An outlying danger is completely circumscribed 
by three lines, each specified according to the same 
principle, and the navigator who knows the three 
clearing lines, but nothing more for certain, takes 
care to keep outside their triangle ; but with more 
minute knowledge he may, when there is occasion, 
cut off a corner of the triangle by guess or by 
feeling his way by the lead. Generally, if the 
danger be of large extent, four or five, or more, 
clearing lines, forming a quadrilateral or polygon 
circumscribing it complelely, are specified, still all 
on the same principle. 

39. There are three serious limitations to the 
complete usefulness and sufficiency of clearing 
marks for pilotage : 

(i.) However well a pilot may know them, still 
he must see two objects for each clearing line, 
one of them generally at a considerable distance. 


It often happens that, through rain or haze, the 
more distant of the two objects is invisible alto- 
gether, although the nearer may be well seen, 
and thus the clearing specification is absolutely 

(2.) A stranger, however well prepared by 
reading his book of sailing directions, must have 
superhuman quickness of perception to always, 
when running at a high speed, recognise with 
sufficient readiness the successive pairs of objects 
constituting the clearing marks for dangers which 
he must skirt along or pass between in his 

(3.) Often while there are good single objects 
to serve as near landmarks visible from the ship's 
course, it may be impossible to find, beyond 
them, any distinct marks, or any marks at all ; 
as when there is too uniform a background of 
hills, or when there is no background at all, the 
land being flat, with no buildings or trees dis- 
tinctly visible in the distance. For one or other, 
or all, of these reasons, the azimuth compass is 
continually in requisition for pilotage. Thus the 


sailing directions always add to the descriptions 
of the two objects which are to be seen in line 
for a clearing mark, a statement of their compass 
bearings when so seen ; also information regard- 
ing soundings when needed, or when available 
as an aid. 

40. I cannot better illustrate the subject, and 
particularly the kind of difficulties which the 
stranger must grapple with, if, aided only by 
sailing directions, he acts as his own pilot, than by 
reading to you from the Admiralty Book of 
Sailing Directions for the West Coasts of France, 
Spain, and Portugal, some extracts regarding the 
entrance to the Tagus over the bar of Lisbon. 
I must premise that " turning through a channel " 
is a technical expression for sailing through the 
channel by a zig-zag course against the wind. 
Directions for turning through a channel neces- 
sarily specify, by proper landmarks, the extreme 
limit to which a ship may safely go on either 
side, from mid-channel, before turning to windward 
for her next tack. 

" Opposite Lisbon, on the south shore, is 


Cassilhas Point, being the eastern point of what 
may be termed the port of Lisbon, and from 
whence the wide expanse already alluded to 
opens out ; here the river is a long mile wide, 
but it narrows to about three-quarters of a mile 
at Belem, when it becomes considerably wider, 

and at its entrance it is if miles across. 

points of the entrance to the Tagus there are 
dangerous sandy shoals extending in a westerly 
direction, and having between them a deep 
channel, which is nowhere less between the 
five fathom lines of soundings than nine-tenths 
of a mile in breadth. The shoals are called 
the North and South Cachopo. 

" From the depth of 4! fathoms, at the west 
end of the North Cachopo, Fort San Julian bears 
about E. by N.JN., distant about 3^ miles. 

" Thence the shoal, with from 2\ to I fathom 
water on it, extends in the direction of the fort, 
leaving at its east end a narrow passage into 
the Tagus, called the North Channel. 


" From the south-east point of entrance to the 
Tagus, the South Cachopo extends to the W. 
and W.S.W. for 2j miles. From the depth of 
4| fathoms, at the west end of the shoal, Bugio 
Fort bears E.N.E. easterly distant if miles. 
The larger portion of this shoal has little more 
than i fathom water on it, and around Bugio 
Fort the sand is dry at low water. 

" The bar between the western extremes of 
the Cachopos, has 6 and 7 fathoms over it at 
low water springs ; the channel within it soon 
deepens to 9 fathoms, increasing to 19 fathoms, 
abreast Bugio Fort. Notwithstanding the depth 
upon the bar, and the distance between the 
extremes of the Cachopos, the sea in S.W. gales 
rolls over it with great force, frequently forming 
one tremendous roller that breaks with irresistible 
violence the whole distance across ; at such times 
the bar is impracticable, and in winter, or w r hen 
the freshes are strong and accompanied with 
westerly gales, continues so for several days 


" Pilots are usually to be found some distance 
from the entrance of the Tagus ; their boats are 
to be distinguished from others by a blue flag 
hoisted at the yard-arm of their lateen sails. 

" LEADING MARKS. Santa Martha Fort, to 
the southward of Cascaes, is white, and of a 
triangular form to the eastward, with a low 
battery extending to the northward ; Guia light- 
house in one with the bastion of this fort, 

N.W.iW., leads through the North Channel. 

" Fort San Julian is an extensive fortification, 
erected on a high steep point on the north-west 
side of the entrance to the Tagus. A ledge of 
rocks, with 3^ fathoms, extends a short distance 
to the south-eastward of the fort. 

" Bugio Fort stands upon the highest part of 
the South Cachopo, about two-thirds of a mile 
from Medao Point, the south-east point of the 
mouth of the Tagus ; the fort is of a circular 
form, and the sand round it is dry at low water. 

" The Paps are very difficult to be distinguished, 
particularly on the bearing used for the South 


Channel, from whence they appear over some 
flat ground, which scarcely shows above the 
land to the south-west of it ; they lie to the 
eastward of a ridge of hills with several wind- 
mills, five of which are close together, then two, 
and just to the eastward of the latter the Paps 
will be found. ' When seen to the northward 
of San Julian, or to the southward of the Bugio, 
they show like two small hummocks, but when 
in a line with either of the turning marks, or 
with the leading mark, they appear as a single 
hummock with a flat top.' 

" The Mirante or Turret of Caxias, is a small 
white building formed of two octagonal turrets, 
with red cupolas, on a hill nearly 3 miles E. by 
N. of San Julian Fort, and is used as the northern 
turning mark for the South Channel when in 
one with the Paps, bearing about E. by N.JN. 

" Jacob's Ladder is a range of black masonry 
or stone wall that supports the cliff, and is not 
easily distinguished, but there is a stone wall 
resembling an aqueduct to the eastward of it, 
and another to the westward. Jacob's Ladder is 


used as the centre leading mark for the South 
Channel when brought in one with the Paps, 
bearing about E. by N.f N. A large conspicuous 
cypress tree stands a third of a mile to the 
eastward of Jacob's Ladder, and when in line 
with the Paps, bearing about E.N.E., is used as 

the southern turning mark for the South Channel. 


" The dome of Estrella is an excellent mark, 
and readily distinguished by its great size, being 
the largest dome in Lisbon, and towering above 
all other buildings in the city ; when in one 

with Bugio Fort it bears E.JN. 


" The South Channel is the principal passage 
into the river. On entering it with a fair wind, 
and rounding the southern extremity of the 
North Cachopo, keep the Peninha (or western 
part of the mountains of Cintra), bearing N.|E., 
and open westward of Cascaes Fort, until Bugio 
Fort comes in one with the Estrella dome E.JN. 
Then steer towards Bugio, keeping it in one with 
the Estrella dome, in which line the bar con- 


necting the North and South Cachopos will be 
crossed in the deepest water, and in not less 
than 6\ fathoms ; and when the Paps are in one 
with Jacob's Ladder, E. by N.fN., a vessel will 
be inside the bar, and the depth of water will 
have increased. Now run up with the Paps in 
one with Jacob's Ladder, or if the wind hangs 
to the northward, borrow as far as the northern 
turning mark (the Paps in one with Caxias, E. 
by N4N.). 

" On the contrary, if the wind be from the 
S.E., borrow towards the southern turning mark, 
with the Paps in line with the cypress tree, 
bearing about E.N.E., but avoid going too near 
Bugio, as the tides there are strong and irregular, 
and the South Cachopo steep-to. 

" Having passed between Bugio and San Julian, 
keep to the northward, so as to clear the sandy 
flat inside Bugio, till Belem Castle is in a line 
with the south part of the city of Lisbon, 
bearing E.f S. Pass Belem Castle at the distance 
of two or three cables, and then proceed to the 
anchorage, keeping the whole of Fort San Julian 


and all its outworks open to the southward of 
the parapet of Belem Castle, which will clear 
the shoals of Alcantara, until the vessel arrives 
off the Packet Stairs, where there is anchorage 
in from 10 to 14 fathoms water, or farther up 
in 12 or 1 6 fathoms, mud. 

A vessel from the north-west standing towards 
the west tail of the North Cachopo, should keep 
Peninha peak, bearing N.JE., open westward of 
Cascaes Fort, and in not less than ' 1 2 fathoms 
water, until the south part of the city of Lisbon 
is in line with Bugio Fort, E.JS. ; then haul to 
the wind. 

" The turning mark for the north side of the 
channel is the Paps, in line with the Mirante or 
Turret of Caxias, E. by NAN. ; and the turning 
mark for the south side of the channel is the 
Paps, in line with the cypress tree (which stands 
a third of a mile eastward of Jacob's Ladder) 

" The northern turning mark is a safe and 
prudent one, as a vessel will not approach any 

VOL. in. F 


part of the North Cachopo nearer than a quarter 
of a mile ; but the southern turning mark carries 
a vessel within ij half cables of the South Cachopo 
and as the tides here are uncertain, the shoal 
should be approached with caution. It is by no 
means desirable to have a tree for a clearing mark, 
which may be down at any moment ; but the 
mariner in this case, in standing towards the latter 
bank need go but little beyond the line of the 
central leading mark. In places, both the North 
and South Cachopo are steep-to." 

41. The process of "taking angles" by the 
sextant is found useful for finding the ship's place 
when in sight of land. It consists of measuring 
by the sextant, held horizontally, the differences of 
azimuth as seen from the ship (s) of three known 
objects or landmarks (A, B, c). Open the three 
rulers of the station pointer to the measured 
angles ASB, BSC, and then lay it down on your 
working chart, and slip it about till the edges 
of the three rulers pass through the positions 
of A, B, C, as shown on the chart. The centre, or 
pointer of the instrument then shows the place 


of the ship. On account of the great exactness 
attainable by it, this process is valuable when 
greater accuracy is desired than can be obtained 
by the use of the azimuth compass, and when three 
objects or landmarks are available. It is also of 
great value as a means for determining the error 
of the compass. It is continually used in nautical 
surveys ; also frequently in ordinary navigation. 
The sextant is also used for finding the distance of 
the ship from some object of known magnitude, as 
for example a lighthouse tower, or another ship. 
Suppose, for example, the height of the tower from 
its base, or a conspicuous mark near its base, to its 
top to be known to be 100 feet. This at a dis- 
tance of a nautical mile (6086 feet), will subtend an 
angle a little less than 1/60 of the radian. Taking 
the radian as 57'3, dividing this by 6086, and 
multiplying by 60, to reduce to minutes, we get 
5 6'* 5 as the angle, subtended by 100 feet, seen 
at a distance of a nautical mile. Hence we have 
the rule : Multiply the magnitude of the object in 
feet by '565, and divide by the angle which it 
subtends ; the result will be the distance in miles. 

F 2 


This method is much used by naval officers to 
measure the distance at any moment from the 
admiral's ship, or some other ship, when sailing in 
squadron, as an aid to keeping in station. 


42. Before attempting to explain Astronomical 
Navigation, I must tell you something of the earth 
as a whole. 

When you look at the hills you see that the 
earth is not exactly globular ; but if I could show 
you an exact model of the size of this large globe be- 
fore you (of two feet diameter), with every mountain 
chain, and hill, and valley, and tree, and building 
constructed exactly to scale, and with the whole sea 
solidified in the form ruffled by waves, precisely as 
it is at any instant, you could not perceive without 
minute and careful examination, that it was any- 
thing different from an exact sphere. The 
Himalayas and Andes would be barely perceptible 
roughnesses, the highest of them being about I 60 
of an inch. The greatest buildings of the world, 


St. Peter's Church at Rome and the Great 
Pyramids, would be utterly imperceptible to touch, 
but would be seen by aid of a powerful microscope. 
The great chimney at St. Rollox would be an 
exceedingly fine thorn of one hundred-thousandth 
of an inch long, and therefore imperceptible to 
touch. The sea would seem a perfectly unruffled 
and brilliant mirror. The figure, however, would 
not be exactly spherical, even though the 
mountains were smoothed off. It would be found 
that the diameter from pole to pole is less by 
about a three-hundredth part than diameters 
through the equator. Thus on the model an 
accurate circular gauge, just fitting over the ends 
of any diameter through the equator, and passing 
round the poles, would show a depression of about 
a three-hundredth of a foot (or 1/25 of an inch) at 
each pole, gradually diminishing to nothing at the 

Were it not for this flattening of the solid at the 
poles and protuberance at the equator, the sea 
would not be distributed as it is, partly in polar 
and partly in equatorial regions, but in virtue of 


centrifugal force would lie almost entirely in a belt 
round the equator, leaving a great island of dry 
land round each pole. 

43. In elementary books on geography, as- 
tronomy, and navigation, terrestrial latitudes and 
longitudes, and meridians, and horizontal planes, 
and verticals and altitudes, are commonly de- 
fined on the supposition that the earth is an exact 
sphere. I prefer definitions of a more practical 
kind, which, be the figure of the earth what it may, 
shall designate in each case the thing found when 
the element in question is determined in practice 
by actual observation. 

(i.) A vertical in any place is the direction of 
the plumb line there, when the plummet hangs at 
rest. The zenith is the point of sky vertically 
overhead, or the point in which the vertical 
produced upwards, cuts the sky. 

(2.) Any plane through a vertical is called a 
vertical plane. The prime vertical is a vertical 
plane perpendicular to the meridian, that is to say, 
it is an east and west vertical plane. 

(3.) The vertical plane in any place passing 


through the point of the sky defined as the 
celestial pole ( 1 1 above) is the meridian of 
that place. 

(4.) A horizontal plane is a plane perpendicular 
to the plumb-line or vertical ; or it may be defined 
as a plane surface of mercury, or water, or other 
liquid, in a basin large enough to give a middle 
portion of liquid surface, not sensibly disturbed 
by the capillaVy action which curves the liquid 
near the sides of the vessel ; yet not so large as to 
show any sensible influence from the curvature of 
the earth. Either a plummet or a basin of liquid 
is practically used for finding horizontal planes or 
horizontal lines. 

(5.) The altitude of any object, terrestrial or 
celestial, as seen from any point of view, is the 
angle between a line drawn to the object and 
a horizontal line in the same vertical plane with 
it ; or it is the angle between the line going 
to the object and the nearest horizontal line ; 
or, as it is sometimes put, it is the inclination to 
the horizontal plane of a line directed to the 


(6.) The latitude of a place is the altitude there 
of the celestial pole. 

(7.) The longitude of a place is the angle between 
its meridian and that of Greenwich. 

(8.) In the preceding definitions the term sky is 
used so as strictly to mean a spherical surface of 
infinitely large radius, having its centre at the centre 
of the earth, or at the eye of an observer situated 
anywhere at the surface of the earth. The great- 
ness of the radius makes it a matter of no moment 
whether the centre be at the earth's centre or at 
the eye of the observer. 

44. (9.) Horizon, derived from a Greek word, 
which signifies bounding, is the boundary between 
sky and earth, or sky and sea, as seen by any 
observer. The term is not usually applied where 
the sky is cut off by high hills or mountains, but 
it is usually and properly enough applied to the 
boundary between earth and sky, as seen by an 
observer looking over a wide extent of level 
country from any elevation, great or small. The 
most common application of the term is to the 
sea horizon, as described in 5 above. Some- 


times "horizon" is used to designate the actual 
line of earth or sea which is seen in line with the 
sky, that is to say, the boundary of the visible 
portion of the surface of earth or sea ; sometimes, 
again, " the horizon " means the boundary line of 
the ideal celestial sphere, separating the visible 
part of it from the part eclipsed by the earth or 
sea. This little ambiguity does no harm. When 
we speak of the distance of the horizon, an ex- 
pression frequently used in navigation, horizon has 
its terrestrial signification. When we speak of 
the distance of a star from the horizon, it is the 
heavenly horizon that we mean. 

45. (10.) A nautical or geographical mile is 
the length of one minute of longitude at the 
equator, and contains 6086 feet or 1014 fathoms. 
This is very nearly the average length of a minute 
of latitude, as the approximately elliptic quadrant 
from the equator to either pole is very nearly 
equal in length to the quadrant of the equator. 
At the equator the length of a minute of latitude 
is less by 1/150, and at the pole it is greater by 
i 150 than the minute of longitude at the equator. 


Thus the actual length of a minute of latitude 
at the equator is '993 of the geographical mile, 
at the pole it is 1*007 geographical miles. Ac- 
cording to the foundation of the French metrical 
system, the length of any meridional quadrant of 
the earth or of a quadrant of the earth's equator 
is very approximately, nearly enough for all 
practical purposes of geography and navigation, 
equal to 10,000,000 metres or 10,000 kilometres. 
Thus 10,000 kilometres are equal to 5,400 nautical 
miles, and as one kilometre is equal to '54 of a 
geographical mile, a geographical mile is equal 
to I '85 kilometres. The existence of the British 
statute mile (5280 feet!) is an evil of not incon- 
siderable moment to the British nation. I shall 
never use the unqualified expression u mile" in 
this lecture, nor, indeed, I hope on any other 
occasion, as meaning anything else than the 
geographical or nautical mile. The mean equa- 
torial diameter of the earth is 6,876 miles, the 
diameter from pole to pole is 6,853 miles. There are 
60 times 360 or 21,600 minutes in the circumference 
of a circle, hence the earth's circumference, which 



is very approximately the same round a meridian 
or round any geodetic line, 1 as round the equator, 
is 21,600 miles. 

The accompanying diagram represents any 
section through the earth's centre. HH' are two 

points of the terrestrial or sea horizon, as seen 
from a point P, at a height of 1/81 of the earth's 
diameter, that is to say, a height of nearly 85 miles. 
PH, the distance of the horizon, is 1/9 of the earth's 
diameter or 762*6 miles. The angle LPH is the 

1 If a line on a given surface be such that a part of it, on each side 
of any point of it whatever, is the shortest distance on the surface 
between the two ends of this part, then it is a geodetic line. 


dip of the horizon. Let HC be the vertical through 
H, meeting the vertical through P in C, then the 
lines CP and CH being perpendicular to LP and 
HP respectively, LP and HP must have the 
angle between them, HCP equal to the angle 
LPH. Considering the earth as approximately 
spherical and gravitation approximately always 
towards its centre, we thus see that the dip of the 
horizon is the angle subtended at the centre by 
the distance of the horizon from the point of 
view. In the case represented in the drawing, PH 
is 2/9 of the radius HC, and therefore obviously 
the angle HCP is very approximately 2/9 of the 
radian, or (2 x S7'3)/9 = I2 7> which therefore is 
the dip of the horizon for a point of view 85 miles 
above the sea. 

To find the distance of the horizon generally, 
multiply the height of the point of view by the 
sum of the height and the earth's diameter, and 
take the square root of the product. This rule is 
applicable to any height however great. When 
the height is not more than a few miles, it is not 
worth while to add it to the earth's diameter. 


Thus, the square root of the number of miles in 
the earth's diameter being 8 2 '8, we have very 
approximately the distance of the horizon in 
miles, equal to 82'8 times the square root of the 
height in miles, or ro6 times the square root of 
the height in feet. To find the distance of the 
horizon in feet, multiply the square root of the 
height in feet by the square root of the diameter 
in miles, and divide the result by 78. 

To find the dip in decimal of the radian, divide 
the distance of the horizon by the earth's radius ; 
or (as we see by using the preceding rules for 
distance), divide the square root of the height by 
the square root of half the radius. Thus the dip 
in radians is equal to the square root of the height 
in miles, divided by 41*4, or is equal to the square 
root of the height in feet divided by 3230. The 
amount of the dip must be subtracted from the 
observed altitude to find what it would have been 
if the observation had been made from a true 
horizontal plane instead of from the dipping 
visual cone, along which the observer looks to his 


46. (11) The refraction, of light is the change 
of direction which a ray is found to experience 
in passing from one transparent medium as 
luminiferous ether, 1 or air or water, to another 
transparent medium, as air or water or glass. 
Light entering the earth's atmosphere from 
the sun or moon or stars, in any other direc- 
tion than the vertical experiences refraction, by 
which its inclination to the vertical is diminished 
as it passes through denser and denser strata of 
the atmosphere down to the surface. Hence every 
observed altitude must be corrected for refraction, 
in order that the true altitude of the straight line 
from the object to the observer may be determined. 
The correction is clearly greater the farther the 
object is from the zenith. The amount of the 
correction is 33' when the line of vision is 
horizontal. In this case the object is actually 
below the horizon by this amount, so that a ray 

1 Luminiferous ether is a name given to the substance, ether or 
aether, occupying space outside some indefinite limit, perhaps 20, 
perhaps 50, perhaps 100 miles high, within which the earth's 
sensible atmosphere is contained. 


entering from the luminiferous ether in a straight 
line which, if continued, would pass over the 
observer's head is bent so as to reach his eye 
horizontally, and to make the object seem on the 
horizon. The denser the air is, the greater is the 
refraction ; and therefore, when, as in " lunars " 
(56 below), extreme accuracy in the allowance for 
refraction is required, the height of the barometer 
and thermometer must be noted at the time of the 
observation. The higher the barometer and the 
lower the thermometer, the greater is the amount 
of refraction. Books on navigation give the 
amount of refraction for different altitudes, for 
mean temperature and mean height of the 
barometer, and auxiliary tables for correction 
according to the actual heights of the baro- 
meter and thermometer at the time of observa- 

47. If the earth were perfectly symmetrical 
round its axis of rotation, like a body turned in a 
lathe, the lines of equal latitude would be exact 
circles in parallel planes perpendicular to the earth's 
axis. They are not exactly so in reality, because 


of the disturbance in the directions of verticals at 
different parts of the earth's surface, produced by 
the attraction of mountains and continents, and 
the defect of attraction of great depths of the sea, 
and by unknown variations of density in the solid 
earth below the bottom of the sea, and below the 
visible surface of dry land. But they are nearly 
enough so for all the purposes of practical 
navigation ; and therefore lines of equal latitude on 
the earth's surface are habitually called circles of 
latitude, or parallels of latitude. 

According to the same supposition of symmetry 
round an axis, the meridian plane of any locality 
would pass through the earth's axis of rotation, 
and it would be the meridian also of every other 
place on the line in which it cuts the earth's 
surface. This result of the imagined symmetry is 
nearly enough true in reality for navigation, and ac- 
cordingly in navigation it is allowable and usual to 
regard lines, in which the earth's surface is cut by 
planes through its axis, as lines of equal longitude ; 
and farther, these lines are often called meridians, 
or terrestrial meridians, there being a habitual 


ambiguity in the use of the word meridian, 
according to which it is sometimes used for a line 
on the earth's surface, and sometimes for the north 
and south vertical plane denned above an am- 
biguity not very inconvenient when we are on our 
guard against any mistake which could arise from 
it. It is exceedingly interesting, in respect to the 
theory of gravitation and of the earth's figure, 
though of no moment in respect to navigation, 
to remark that, in reality, lines of equal longitude 
are not precisely meridional lines, or true north 
and south lines ; ?nd that lines of equal latitude 
are not exactly circles, but slightly sinuous curves. 
48. Just two kinds of observation are used in 
astronomical navigation which are shortly desig- 
nated as " altitudes " and " lunars" I shall say 
nothing of lunars at present, except that they are 
but rarely used in modern navigation, as their ob- 
ject is to determine Greenwich time, and this object, 
except in rare cases, is nowadays more correctly 
attained by the use of chronometers than it can 
be by the astronomical method. 

The astronomical observation, which is practised 
VOL. in. G 


regularly by day and frequently also at night in 
practical navigation, consists simply in measuring 
by the sextant the apparent altitude of the sun or 
star above the horizon ( 5 above) and noting 
accurately the hour, minute, and second by the 
ship's chronometer, at which the observation is 
taken. The immediate results of the observation 
are corrected according to explanations I have 
already given you in respect to the following 
several particulars index-error, dip of the horizon, 
and refraction ; also for the sun's semi-diameter, 
when it is the sun, not a star, that is observed. 

49. LATITUDE. With these definitions and 
explanations premised, we are prepared to under- 
stand readily how latitude and longitude are 
determined by actual observation of stars or sun. 
If there were a bright enough star exactly at the 
celestial pole of whichever hemisphere we are in, 
we should only have to observe its altitude above 
the horizon, and that would be the latitude. In 
the northern hemisphere, Polaris, as I have told 
you, is seen describing daily a small circle of i 21' 
distance from the true north celestial pole ; and 


therefore, if you are satisfied with knowing your 
latitude within i 21', the simple altitude of Polaris 
gives it. But if you know the sidereal time of 
your observation, even very roughly, say within 
five or ten minutes of time, you can calculate the 
correction required to give the true latitude from 
the observed altitude of Polaris accurately enough 
for practical purposes. 1 . This method is practised 
very frequently at sea in the northern hemisphere. 
The meridian altitude of any known star, or of the 
sun, gives the latitude, for the Nautical Almanac 
tells v you the distance 2 of the observed body from 

1 The greatest error in the deduced latitude due to error in your 
reckoning of time is, of course, to be met if the observation is made 
when the star is rising or sinking with the greatest rapidity that is 
to say, when it has made a quarter of its revolution from the lowest 
or highest points of its diurnal circuit. At such times there is an 
error of 2' latitude for six minutes' error in your reckoning of time. 

2 The Nautical Almanac gives what is called the declinations of 
stars and sun, that is, the angular distance north or south from the 
celestial equator, this being a plane through the observer's eye perpen- 
dicular to the axis of the earth's rotation. The north polar distance 
is found by subtracting the declination from, or adding it to, 90, 
according as it is north or south declination. Thus the declination 
of Arcturus is 19 50' N. ; its north polar distance, therefore, is 
70 10' N. Again, the declination of the sun to-day (Nov. u, 1875) 
is 17 24' S ; his north polar distance, therefore, is 107 24'. 

G 2 


the celestial pole at the time of your observation. 
From the observed altitude, then, of the stars or 
sun, you can deduce the altitude of the pole 
thus : 

1. If the star crosses the meridian under the 
pole, add the polar distance to the observed 

2. If the star crosses the meridian above the 
pole, but north of your zenith, subtract its polar 
distance from the observed altitude. 

3. If star or sun cross the meridian south of 
your zenith, add its polar distance to the observed 
altitude and subtract the sum from 180. 

So, in any one of the three cases the latitude 
is calculated from your observation. 

In meridian observations for the latitude the 
aid of the chronometer is not needed : the 
observer keeps watching the altitude by aid of 
a sextant till he finds it cease to diminish and 
begin to increase (in case No. i), or till he finds 
it cease to increase, and begin to diminish (in 
case 2 or case 3). He thus finds, as nearly as 
he can in each case, the least altitude or the 


greatest altitude, as the case may be. Practically, 
he does help himself by finding by the aid of 
his Nautical Almanac the time on his watch 
within a few minutes of the precise instant when 
the least or greatest altitude is to be observed ; 
but then, though the altitude changes but very 
little within five or ten minutes, before and after 
this instant, the observer generally satisfies himself 
that he has got the true minimum or the true 
maximum by waiting till he finds the change 
from sinking to rising, or rising to sinking. 

50. LONGITUDE. To determine the longitude 
by astronomical observation, two things must be 
done. The local time must be found from sun 
or stars, and Greenwich time taken at the same 
instant from your chronometer, or, failing the 
chronometer, by lunars. The difference of the 
times thus found reduced to angle at the rate 
of 15 to the hour, 15' of angle to one minute 
of time, 15" of angle to one second of time, is 
your longitude east or west of Greenwich, ac- 
cording as your local time is before or behind 
Greenwich time. On shore local time is most 


accurately found by observing the instant when 
the sun or a star crosses the meridian. But on 
board ship this method cannot be practised, and 
instead an altitude, whether of sun or star, is 
observed when the body is anywhere out of the 
meridian. Now remember that a star (or, neg- 
lecting a very slight error due to change of 
declination, the sun) is at its greatest altitude 
when it is crossing the meridian, and you will 
understand that, when the observed altitude is 
anything less than the greatest altitude, you can 
calculate how long time before or after its 
meridian passage, must have been the instant of 
your observation. The calculation requires a 
knowledge of the declination of the observed 
body, and of the latitude of the ship's place at 
the time of the observation ; but if you have 
chosen a star in the prime vertical, or very 
nearly in the prime vertical, a very rough ap- 
proximation to your latitude suffices. The 
method most commonly practised at sea is to 
estimate the latitude as accurately as possible by 
dead reckoning from previously determined 


positions, to use this latitude in determining 
local time from an observation of altitude, and 
thence by chronometer to determine the longitude. 
But, except any case in which the observed body is 
on the prime vertical at the instant of observation 
(and for every such case, the old ordinary method 
is virtually equivalent to Sumner's method), that 
method is not, and Sumner's method (to be ex- 
plained later) is, the simple and direct interpretation 
of what you learn as to the ship's place from an 
observation of altitude (see Art. 5 above). 

time of the instant of observation is to be cal- 
culated according to the known error of the 
chronometer or the mean of the errors of several 
chronometers, w r hen there are several on board. 
Now, what is the inference to be made from the 
fact that the altitude of the sun's centre above a 
true horizontal plane through the ship was so and 
so say 40 at such and such a time, say on the 
2;th of August 1874, at IH. 2IM. 23$. P.M. mean 
Greenwich time ? It is simply this, that the 


ship at the time of observation was somewhere 
on a certain circle of the earth at every point of 
which the sun's altitude was the same. To draw 
this circle on a drawing globe, such as the black 
globe before you, you must find first at what 
point of the earth the sun was overhead at the 
instant of observation. This you do immediately 
by aid of the Nautical Almanac, which gives you 
the instant of the sun's being due south at Green- 
wich every day of the year. Thus on the 27th of 
August 1874 the sun "southed" at Greenwich at 
I2H. IM. 238. P.M.; therefore in a place in west 
longitude 20, he was due south at the instant 
of observation. His declination was 10 N., hence 
he was overhead in lat. 10 N., Ion. 20 W. Put 
one point of the compasses at the corresponding 
point of your drawing globe, and draw by aid 
of the compasses a circle running at 40 of the 
earth's surface from this point. The ship was 
somewhere on this circle at the instant of the 
observation. The chart before you shows this 
circle drawn on Mercator's projection not a true 
circle as you see, because circles on the earth's 



surface are not shown as circles on Mercator's 

Suppose now that 2H. 4OM. later the altitude of 
the sun is again taken and found to be 50. At 
the moment of this second observation, the ship 
was on this other circle which you see on the 

I2O IOO 80 60 40 2O O 2O 40 60 

FIG. 14. Mercator chart, showing Sumner circles. 

chart. What we learn from the two observations 
then is, that at the time of the first observation 
the ship was somewhere on that first circle, and 
that at the time of the second observation she 
was somewhere on that second circle. These 


circles are called by Sumner circles of equal 
altitude. The portions of them shown on your 
working chart are conveniently called Sumner 
lines. Now simply by dead reckoning estimate 
the course and distance made by the ship in the 
interval between the two observations. Take a 
length equal to this distance, and by aid of a 
parallel ruler place it in proper direction, with one 
end of it on one of the Sumner lines, and the other 
on the other. The two ends of the line show the 
places of the ship at the instants of the two 

The process of drawing on a globe which I put 
before you is, you must understand, merely put 
by way of illustration of the principle. It would 
be practically impossible, or at all events so 
difficult as to be impracticable, to carry out the 
construction at sea by means of compasses on 
a globe, or by ruler and compasses on a plane 
chart, with sufficient exactness to give the ship's 
place as accurately as it can be determined from 
the observations. Calculations by what is called 
spherical trigonometry, therefore, must take the 


place of drawing by ruler and compasses ; and it 
is by calculation that the ship's place is found every 
day at sea from the observations of altitude. The 
ordinary mode of calculation is given in full in 
every book on navigation and need not be repeated 
to you by me. 

52. The clear and obvious mode of interpreting 
the information derivable from a single altitude of 
the sun or stars which I have put before you, 
is due to Captain Thomas B. Sumner of Boston, 
Massachusetts. It is not only valuable as giving 
us a clear view of the geometrical process under- 
lying the piece of calculation by logarithmic tables 
which is performed morning and evening by the 
practical navigator at sea, but it actually gives 
him a much more useful practical way of working 
out the results of his observations than that which 
is ordinarily taught in schools and books of 
navigation, and ordinarily practised on board ship. 
It is too usual to wait for the noon observation 
before working out the result of the morning 
altitude. Instead of this, the Sumner line ought to 
be calculated for each observation independently, 


and drawn on the ordinary working chart. Then 
the navigator knows that the ship is somewhere on 
that line, even though he may not know his 
latitude within twenty or thirty miles. 

I have known a case of a ship bound from South 
America to England, intending to call at Fayal, 
Azores, for provisions, and being saved from passing 
out of sight of the island before noon by the 
Sumner line, calculated from observation at seven 
in the morning. This observation proved the ship 
to be about eleven miles further west than estimated 
from the afternoon observation of the previous day ; 
and a timely change of the course, three points 
to the eastward at eight o'clock, brought the heights 
of Fayal in view ahead about half-past ten. If 
the ordinary course had been held on till noon, 
the ship would then have been eleven miles 
to the west of the west end of Fayal, and the 
island still unseen as the weather was somewhat 
cloudy ; and the ship must have been turned 
round at right angles to her course to look for 
the island. 

53. Having been much impressed with the value 


of Sumner's method, from seeing the valuable 
results of the skilful use made of it by Captain 
Moriarty, R.N., in the Atlantic cable expeditions 
of 1858, 1865, and 1866, and particularly in finding 
the places for the successive grapplings by which 
the lost 1865 cable was recovered and completed 
in 1866, I have long felt convinced that it ought 
to be the rule and not the exception to use 
Sumner's method for ordinary navigation at sea. 
I have therefore prepared tables, copies of which 
I hold in my hand, for facilitating the practice 
of Sumner's method at sea, and have had them 
printed and "stereotyped for publication. The pub- 
lication only waits the preparation and printing of 
the pamphlet of rules and illustrations to explain 
how they are to be used. 1 

The practice of Sumner's method for star ob- 
servations is even more valuable than for the 
altitudes of the sun taken by day. By taking 
the altitudes of two stars at the same time, or 

1 The pamphlet of rules and illustrations is now (April, 1876) in 
type, and nearly ready for press. It will, with the stereotyped tables, 
be published in the course of a few weeks by Messrs. Taylor and 
Francis, London. 


within so short a time one after the other that the 
ship has not travelled far in the interval, we 
get two Sumner lines on our chart, and know 
that, at the time of the observations, the ship 
was actually on the point in which the two lines 

Thus on a clear night we can at any time find 
the ship's actual place, as we can always choose 
two good stars in good positions for the purpose ; 
while by day, all we can tell, as we have only one 
sun and no other visible body (except sometimes 
the moon, which is not very convenient for such 
observations), is that the ship is on a certain 
line, viz., the Sumner line for the moment of 
observation. If, then, we could observe the al- 
titudes of stars with the same accuracy as the sun, 
we could know the ship's place better by night 
than by day ; but, alas, the observation of the star 
altitude is rarely to be made with all the desired 
accuracy, even by the most skilful observer, because 
it is so difficult at night to see precisely where 
the sea-horizon is. 



word about latitude before leaving Sumner's 
method, the beauty of which, according to Captain 
Croudace of Dundee, a very intelligent advocate 
of it, 1 " consists in its glorious disregard of the true 
latitude." You see that, in describing it, I have 
never once used the word latitude ; but now what 
I have to say is this : If the altitude is taken 
when the sun is exactly in the meridian, the 
Sumner circle touches the circle of latitude in 
which the ship is at the time, and therefore the 
information which in this case we derive from 
Sumner's method, is simply the ship's latitude. 
Thus we see that the old well known and universal 
way of finding a ship's latitude is only a particular 
application of Sumner's method. But there is 
this peculiarity of the noon observation : you do 
not need to take time from a chronometer 
when making it ; all you have to do is to find 
the greatest altitude attained by the sun just 
before he begins to dip. Should he be clouded 
over at the critical moment when he is highest 

1 Star Fontm/at y for Finding Latitude and Longitude by Sumner's 
Method, p. 4, Preface. By W. S. Croudace. 


above the horizon, the meridian altitude is lost, 
and Sumner's method, or something equivalent to 
it, must be put in requisition. When the meridian 
observation is lost, but instead of it the altitude 
within half an hour before or after the sun crosses 
the meridian is observed, it is usual to employ a 
a table, which is given in the books on Navigation, 
for computing what is called " reduction to the 
meridian," that is to say, the addition which must 
be made to the observed altitude to find the true 
meridian or highest altitude ; but in practice it 
is really much better to draw the Sumner line of 
the actual observation on the chart, and judge from 
it what the observation has really told you as to 
the ship's position. 

55. The chart before you (Fig. 15) illustrates 
Sumner's method by an actual case of its use in 
ordinary navigation, in a voyage from Falmouth to 
Madeira, made by the sailing yacht Lalla Rookh, 
from the 3rd to the Qth of May, 1874. The times 
marked on the several Sumner's lines are the 
Greenwich mean times of the observations. Look 
carefully at the positions of the Sumner day-lines, 



as shown on the chart, and by considering the 







FIG. 15 Chart showing Suinner lines on a voyage Falmouth to Madeira, 

longitudes at the several places, the Greenwich 
mean times marked, and the equation of time which 


was from three to four minutes " sun behind time," 
you will understand exactly how each line lies 
as you see it on the chart, being, as I have told you 
before, always in a direction perpendicular to the 
line from the ship, to the point on the horizon 
under the sun. 

Look again at the lines determined by altitudes 
of Polaris and Arcturus, observed on the night 
before reaching Cape Finisterre. You see how 
they intersect exactly in the place where the 
vessel was at the time, and can understand how 
important the full information thus given was in 
the case of approaching land. Porto Santo was 
sighted at noon on the pth of May, and Madeira 
two hours later. No more astronomical obser- 
vations were needed. 

56. LUNARS. I have spoken to you of the 
marvellous accuracy of the marine chronometer, but 
till Harrison's invention of the first useful artificial 
marine chronometer, fulfilling Sir Isaac Newton's 
anticipation, was given to the world, in 1765, 
through the well-judged beneficence of the British 
Government, the only chronometer generally avail- 


able for finding longitude at sea was that great 
natural chronometer presented by the moon in 
her orbital motion round the earth. 

Imagine a line joining the centres of inertia 
of the earth and moon to be, as it were, the 
hand of a great clock, revolving round the 
common centre of inertia of the two bodies, 
and showing time on the background of stars 
for dial. If the centres of inertia of the moon 
and earth moved uniformly in circles round the 
common centre of inertia of the two, the moon, 
as seen from the earth, would travel through equal 
angles of a great circle among the stars in equal 
times ; and thus our great lunar astronomical 
clock would be a perfectly uniform timekeeper. 
This supposition is only a rough approximation 
to the truth ; and the moon is, in fact, a very 
irregular chronometer. But thanks to the mathe- 
maticians, who, from the time of Newton, have 
given to what is called the Lunar Theory in 
Physical Astronomy the perfection which it now 
possesses, we can tell, for years in advance, 
where the moon will be relatively to the stars, at 

H 2 


any moment of Greenwich time, more accurately 
than it can be observed at sea, and almost as 
accurately as it can be observed in a fixed ob- 
servatory on shore. Hence the error of the clock 
is known more exactly than we can read its 
indications at sea, and the accuracy with which 
we can find the Greenwich time by it, is practically 
limited by the accuracy with which we can ob- 
serve the moon's place relatively to the sun, 
planet, or star. This, unhappily, is very rough 
in comparison with what is wanted for navigation. 
The moon performs her orbital revolution in 
27-321 days, and, therefore, moves at an average 
rate of o'55 P er hour, or '55 of a minute of angle 
per minute of time. Hence to get the Greenwich 
time correctly to one minute of time, or longitude 
within 15 minutes of angle, it is necessary to 
observe the moon's position accurately to half 
a minute of angle. This can be done, but it is 
about the most that can be done in the way of 
accuracy at sea. It is done, of course, by measur- 
ing, by the sextant, the angular distance of the 
moon from a star, as nearly as may be in the 


great circle of the moon's orbital motion. Thus 
supposing the ship to be navigating in tropical 
seas, where a minute of longitude is equal to a 
mile of distance, a careful navigator, with a good 
sextant, whose errors he has carefully determined, 
can, by one observation of the lunar distance, 
find the ship's place within fifteen miles of east 
and west distance. If he has extraordinary skill, 
and has bestowed extraordinary care on the de- 
termination of the errors of his instrument, he 
may, by repeated observations, attain an accuracy 
equivalent to the determination of a single lunar 
distance within a quarter of a minute of angle, 
and so may find the ship's place within seven 
miles of east and west distance ; but, practically 
we cannot expect that a ship's place will be found 
within less than twenty miles, by the method of 
lunars in tropical seas, or within ten miles in 
latitude 60 ; and to be able to do even so much 
as this is an accomplishment which not even a 
good modern navigator, now that the habit of 
taking lunars is so much lost by the use of 
chronometers, can be expected to possess. 


57. The details of the method of lunars, the 
practical mastery of which used to be the great 
test of a good navigator before the time of 
chronometers, are beyond the scope of the present 
lecture. I must limit myself to telling you that 
from rough observations of the altitudes of the 
two bodies, moon, and sun or planet or star, and 
observations of the barometer and thermometer, 
the effects of atmospheric refraction in altering 
the apparent distance between the two bodies 
must be calculated. By an approximate know- 
ledge of the ship's position, the difference between 
the observed distance and that which would have 
been observed if the place of observation had been 
the earth's centre, must be determined. 

The application of these corrections for refrac- 
tion and parallax, so as to find, from the observed 
distance, the actual angle between the line going 
from the earth's centre to the moon's centre, 
and the line from the earth's centre to the other 
body, is what is technically called " clearing the 

58. The books on navigation used at sea 


(Inman, Norrie, and Raper) contain carefully 
elaborated rules and sets of tables for the pur- 
pose of making the practical problem of clearing 
the distance as easy as possible. The conclusion 
of the process of finding Greenwich time by a 
lunar observation at sea I can best explain to you 
by reading from the Nautical Almanac for 1876, 
page 511, premising that six pages of the Nautical 
Almanac are devoted to data for finding the longi- 
tude at sea by the method of lunars. 

"Pages XIII. to XVIII. of each month, Lunar 
" Distances, These pages contain, for every third 
" hour of Greenwich mean time, the angular 
" distances available for the determination of the 
" longitude of the apparent centre of the moon 
" from the sun, the larger planets, and certain 
" stars, as they would appear from the centre of 
" the earth. When a lunar distance has been 
" observed on the surface of the earth, and re- 
" duced to the centre by clearing it of the effects 
" of parallax and re/raction, the numbers in these 
" pages enable us to ascertain the exact Greenwich 
" mean time at which the objects would have 


" the same distance. They are arranged from 
" west to east, commencing- each day with the 
" object which is at the greatest distance west- 
" ward of the moon, in the precise order in 
" which they appear in the heavens ; W. indicating 
" that the object is west, and E. east of the moon. 

" The columns headed * P. L. of cliff.' contain 
" the proportional logarithms of the differences 
" of the distances at intervals of three hours, 
" which are used in rinding the Greenwich time, 
" corresponding to a given distance, according to 
" the following rule, viz. : For the given day, 
" seek in the Ephemeris for the nearest distance 
"preceding, in order of time, the given distance, 
" and take the difference between it and the 
" given distance ; from the proportional logarithm 
" of this difference, subtract the proportional 
" logarithm in the Ephemeris ; the remainder will 
" be the proportional logarithm of a portion of 
" time to be added to the hour answering to the 
" nearest preceding distance, to obtain the ap- 
" proximate Greenwich mean time corresponding 
" to the given distance. 


" If the distance between the moon and a star 
" increased or decreased uniformly, the Greenwich 
" times corresponding to a given distance, as 
" found by the above rule, would be strictly 
" correct ; but an inspection of the columns of 
" the proportional logarithms in the Ephemeris 
" will show that this is not the case ; a correction 
" must therefore be applied to the time so found 
" for the variation of the difference of the 
" distances. This correction may be obtained 
u by means of the table at page 490 of the 
" present volume, in the following manner." 

[Here follow details of the method of inter- 
polation to be used with examples of its 


59. I have now explained to you briefly, and 
very imperfectly, navigation in clear weather. I 
must next speak to you on a more sombre part 
of our subject, navigation under clouds or through 
fog. When no landmarks can be seen, and when 


the water is too deep for soundings, if the sky 
is cloudy so that neither sun nor stars can be 
seen, the navigator, however clear the horizon 
may be, has no other way of knowing where he 
is than the dead reckoning, and no other guide 
for steering than the compass. 

We often hear stories of the marvellous exact- 
ness with which the dead reckoning has been 
verified by the result. A man has steamed or 
sailed across the Atlantic without having got a 
glimpse of sun or stars the whole way, and has 
made land within five miles of the place aimed 
at. This may be done once, and may be done 
again, but must not be trusted to on any one 
occasion as probably to be done again this time. 
Undue trust in the dead reckoning has produced 
more disastrous shipwrecks of seaworthy ships, I 
believe, than all other causes put together. All 
over the surface of the sea there are currents of 
unknown strength and direction. Regarding these 
currents, much most valuable information has 
been collected by our Board of Trade and 
Admiralty, and published by the Admiralty in 


its "Atlas of Wind and Current Charts." These 
charts show, in scarcely any part of the ocean, 
less than ten miles of surface current per twenty- 
four hours, and they show as much as forty or 
fifty miles in many places. Unless these currents 
are taken into account then, the place of a ship, 
by dead reckoning, may be wrong by from ten 
to fifty miles per twenty-four hours ; and the 
most accurate information which we yet have 
regarding them is, at the best, only approximate. 
There are, in fact, uncertain currents, of ten miles 
and upwards per day, due to wind (it may 
be wind in a distant part of the ocean) which 
the navigator cannot possibly know at the time 
he is affected by them. I believe it would be 
unsafe to say that, even if the steerage and the 
speed through the water were reckoned with 
absolute accuracy in the "account," the ship's 
place could in general be reasonably trusted to 
within fifteen or twenty miles per twenty-four 
hours of dead reckoning. And, besides, neither 
the speed through the water, nor the steerage, 
can be safely reckoned without allowing a con- 


siderable margin for error. In the recent court- 
martial regarding the loss of the Vanguard, the 
speed of the Iron Duke was estimated by one 
of the witnesses at ten and a half knots according 
to his mode of reckoning from revolutions of 
the screw and the slip of the screw through the 
water, while other witnesses, for reasons which 
they stated, estimated it at only 8*2 knots. It 
was stated in evidence, however, that the only 
experiments available for estimating the ship's 
speed in smooth water from the number of 
revolutions of the screw, had been made before 
she left Plymouth. If the old log-ship and glasses 
had been used, there could have been no such 
great range of doubt : or the Massey log, which 
may be held to do its work fairly well if it 
gives the whole distance run by the ship in 
any interval within five per cent, of the truth. 

60. Consider further the steerage. In a wooden 
ship a good ordinary compass, with proper pre- 
cautions to keep iron from its neighbourhood, 
may be safely trusted to within a half-quarter 
point ; but, reckoning the errors of even very 


careful steering by compass, we cannot trust to 
making a course which will be certainly within 
a quarter of a point of that desired. Now you 
know an error of a quarter of . a point in your 
course, would put you wrong by one mile to 
right or left of your desired course for every 
twenty miles of distance run. Thus in the most 
favourable circumstances you are liable, through 
mere error of steerage by compass, to be ten 
miles out of your course in a run of two hundred. 
In an iron ship, if the ordinary compass has been 
thoroughly well attended to as long as the weather 
permitted sights of sun or stars, a very careful 
navigator may be sure of his course by it, within a 
quarter of a point, when cloudy weather comes 
on ; but by the time he has run three or four 
hundred miles he can no longer reckon on the 
same degree of accuracy in his interpretation of its 
indications, and may be uncertain as to his course 
to an extent of half a point or more until he 
again gets an azimuth of sun or star. No doubt 
an exceedingly skilful navigator may entirely, or 
almost entirely, overcome this last source of 


uncertainty when he runs over the same course 
month after month and year after year in the 
same ship ; but it is not overcome by any skill 
hitherto applied to the compass at sea when a 
first voyage to a fresh destination, whether in a 
new ship or in an old one, is attempted. 

All things considered, a thoroughly skilled and 
careful navigator may reckon that, in the most 
favourable circumstances, he has a fair chance 
of being within five miles of his estimated place, 
after a two hundred miles' run on dead reckon- 
ing ; but with all his skill and with all his care, 
he may be twenty miles off it ; and he will no 
more think of imperilling his ship and the lives 
committed to his charge on such an estimate, 
than a skilled rifle-shot would think of staking 
a human life on his hitting the bull's-eye at five 
hundred yards. What, then, do practical navi- 
gators do in approaching land after a few days' 
run on dead reckoning ? Too many, through 
bad logic and imperfect scientific intelligence, 
rather than through conscious negligence, run 
on, trusting to their dead reckoning. In the 

NA VIGA TION. 1 1 1 

course of eight or ten or fifteen years of navi- 
gation on this principle, a captain of a mail 
steamer has made land just at the desired place 
a dozen times, after runs of strictly dead reckon- 
ing- of from three or four hours to two or three 


days. Perhaps of all these times there has only 
once been a strictly dead reckoning of over thirty 
hours with satisfactory result. Still, the man 
remembers a time or two when he has hit the 
mark marvellously well by absolutely dead 
reckoning ; he actually forgets his own prudence 
on many of the occasions when he has corrected 
his dead reckoning by the lead, and imagines 
that he has been served by the dead reckoning 
with a degree of accuracy, with which it is im- 
possible, in the nature of things, it can serve 
any man. Meantime, he has earned the character 
of being a most skilful navigator, and has been 
unremitting in every part of his duty, according 
to the very best of his intelligence and know- 
ledge. He has, moreover, found favour with his 
owners, through making excellent passages in all 
weathers, rough or smooth, bright or cloudy, clear 


or foggy. At last the fatal time comes, he has 
trusted to his dead reckoning once too often, he 
has made a "centre," not a "bull's-eye," and his 
ship is on the rocks. 


61. What then, on approaching land in cloudy 
weather, does the navigator do who is not only 
careful but prudent, not only bold and able but 
also intelligent and well taught, not only devoted 
to the interests of his employers but devoted with 
a knowledge which they can scarcely be expected 
to appreciate ? He simply feels his way by the 
lead, from the time he comes within soundings, 
till he makes the land and makes sure by light- 
house and landmark of where he really is. 

Neither annoyance to the ship's company 
through the extra labour which it entails, nor 
consideration of the detention which it may 
require, prevents him from using the deep sea 
lead at least once an hour, unless he has satis- 
factory grounds for confidence in proceeding with 


less frequent soundings. An admirable method 
of navigation by the lead was recently explained 
to me by Sir James Anderson, who told me he 
was constantly in the habit of using it in his 
transatlantic voyages, and that he found it had 
been independently used by Captain Moriarty, 
R.N. It seems not to be described in any of 
the books on navigation, but it is so simple and 
effective that I think you will be interested if I 
explain it to you. Take a long slip of card, or 
of stiff paper, and mark along one edge of it 
points at successive distances from one another, 
equal, according to the scale of your chart, to 
the actual distance estimated as having been run 
by the ship in the intervals between successive 
soundings. If the ship has run a straight course, 
the edge of the card must oe straight, but if 
there has been any change of direction in the 
course, the card must be cut with a corresponding 
deviation from one straight direction. Beside 
each of the points thus marked on the edge, 
write on the card the depth and character of 
bottom found by the lead. Then place the card 


on the chart, and slip it about till you find an 
agreement between the soundings marked on the 
chart and the series marked on your card. The 
slight ups and downs of the bottom, even if they 
be no more than to produce differences of five or 
six fathoms in depths of, say, from five-and-thirty 
to fifty fathoms, interpreted with aid from the 
character of the bottom brought up, give, when 
this method is practised with sufficient assiduity, 
an admirably satisfactory certainty as to the 
course over which the ship has passed. Sir James 
Anderson tells me that he has run from the 
Banks of Newfoundland for two days through 
a thick fog at twelve knots, never reducing speed 
for soundings, but sounding every hour by the 
deep sea lead and Massey fly, has brought up 
his last sounding black mud opposite to the mouth 
of Halifax Harbour, and has gone in without 
ever once having got a sight of sun or stars all 
the way from England, or of headland before 
turning to go into harbour. 

[Addition of August 4th, 1887. The taking 
of soundings with the ordinary deep sea rope 


when the ship is going at a speed of twelve 
knots, involves so much labour and requires so 
many men to haul in the rope that it would not 
be practicable to take casts more frequently than 
once ever>' hour. The method of navigation with 
the lead, described in the preceding paragraph, was 
only used in very exceptional circumstances. But 
with the wire sounding machine (already referred 
to > 37 above : see on this subject, articles " On 
Deep-Sea Sounding," &c, in present volume), 
this laborious operation is no longer necessary 
The wire offers so very little resistance when 
going through the water that two men can easily 
take a cast in any depth up to 100 fathoms with 
the ship going at any speed up to sixteen knots. 
The whole operation does not take more than 
from two to six minutes, according to the depth, 
so that a sounding can be regularly taken every 
ten minutes.] 

In moderate weather, with her engines in work- 
ing order, and coal enough on board to keep up 
steam, no steamer making land from the ocean, 
in a well explored sea, need ever, however thick 

I 2 


the fog, be lost by running on the rocks. Nothing 
but neglect of the oldest of sailors' maxims, " lead 
log, and look-out," can possibly ever, in such 
circumstances, lead to such a disaster. 

62. But there is a danger affecting navigation 
in all weathers, though with greatest intensity 
in fogs, which no degree of human skill and 
conscientiousness can reduce to absolute zero, 
and ttfat is collision. 

The " Regulations for Preventing Collisions at 
Sea," l which I hold in my hand, embody as in- 
ternational law everything that human wisdom 
has been able to devise up to the present time 
for diminishing the chances of collision. A vast 
majority of the collisions which have taken place, 
have been produced by breach of these rules by one 
ship or the other, or both. 

AT SEA. Here are some of them: "Art. 10. 
Whenever there is fog, whether by day or by 

1 Issued in pursuance of the Merchant Shipping Act Amend- 
ment Act, 1862, and of an Order in Council, dated Qth January 
1863, and adopted by twenty-nine maritime nations by various 
orders, dating from 1st May 1863 to 3Oth Aug. 1864. 


night, the fog signals, described below, shall be 
carried and used, and shall be sounded at least 
every five minutes, viz. : 

" (a) Steam ships under way shall use a steam 
whistle placed before the funnel not less than eight 
feet from the deck. 

" (b) Sailing ships under way shall use a fog- 

"(c) Steam ships and sailing ships when not 
under way shall use a bell. 

"Art 15. If two ships, one of which is a sail- 
ing ship, and the other a steam ship, are proceed- 
ing in such directions as to involve risk of collision, 
the steam ship shall keep out of the way of the 
sailing ship. 

"Art. 1 6. Every steam ship when approaching 
another ship so as to involve risk of collision shall 
slacken her speed, or if necessary stop and reverse ; 
and every ship shall, when in a fog, go at a 
moderate speed. 

"Art. 17. Every vessel overtaking any other 
vessel shall keep out of the way of the said last- 
mentioned vessel. 


"Art. 1 8. Where by the above rules one of 
two ships is to keep out of the way, the other 
shall keep her course, subject to the qualifications 
contained in the following Article. 

" Art. 19. In obeying and construing these 
rules, due regard must be had to all dangers of 
navigation ; and due regard must also be had to 
any special circumstances, which may exist in 
any particular case, rendering a departure from 
the above rules necessary in order to avoid 
immediate danger. 

"Art. 20. Nothing in these rules shall ex- 
onerate any ship, or the owner, or master, or 
crew thereof, from the consequences of any 
neglect to keep a proper look-out, or of the 
neglect of any precaution which may be required 
by the ordinary practice of seamen or by the 
special circumstances of the case." 

Art. 15 makes the duty of the steamer, in the 
case referred to, unmistakable. It is to steer 
in such a way that a collision cannot take place, 
whatever the sailing ship may do. The steamer 
has no right to reckon that the sailing ship will 


continue exactly on an unaltered course, or that 
she will make some seemingly probable alteration 
in her course (as in " turning to windward ") ; in 
short, the steamer must, if possible^ steer in such 
a manner that no action of the sailing vessel 
can bring about a collision. So, of Art. 17, with 
reference to one vessel overtaking another, 

63. Under Arts. 18 and 19, the sailing vessel 
of Art. 15, or the overtaken vessel of Art. 16 may 
commit a fault. It happens often that the sailing 
vessel or the overtaken vessel sees the steamer or 
the overtaking vessel coming dangerously near. 
It is generally impossible to tell whether this is 
done wilfully with the intention of making "a 
close shave," or wilfully with the intention of 
unlawfully compelling the other to give way, or 
unintentionally through total or partial want of 
look-out. If the master of the threatened vessel 
could tell for certain that there was no look-out 
in the other vessel, and that the look-out ivould not 
suddenly wake up, then he could ensure safety by 
a variation of his own course, which then in virtue 
of Art. 19 would not violate Art. 18. But he can 


have no such knowledge. The other vessel may 
suddenly alter her course, whether through the 
look-out wakening up, or through the master per- 
ceiving he has failed in his attempt to unlawfully 
compel the sailing vessel or the overtaken vessel 
to get out of his way, or through a too late 
resolution to do what he ought to have done 
earlier alter his own course. The master of the 
threatened vessel feels he must " do something." 
It seems impossible that he can escape if he holds 
on his course : he alters his course, but does not 
escape collision. He may be blamed under Art. 18, 
or justified under Art. 19, but whether he be 
blamed or whether he be justified, the other is 
certainly culpable for breach of Art. 15 or Art. 17, 
as the case may be. 

It is not an exceedingly rare incident for two 
steamers on the wide ocean, in clear and moderate 
weather, to be on such courses that they cannot 
in the nature of things, escape collision otherwise 
than by the fulfilment of Art. 16. How can a 
man walking towards a mirror escape collision 
with his own image ? Only by slowing and 


stopping. Or two men meeting on a broad path, 
with plenty of room to pass one another, how often 
does it not happen that they can only escape 
collision by one or both stopping ? 

The rule of the road 1 at sea seems to me good in 
almost every particular as it stands in the interna- 
tional regulations, some of which I have just now 
read to you ; and certainly among all the comments 
upon the lav/ relating to them, I have scarcely 
heard any proposal for its improvement except 
national and international provisions for punish- 
ment for breaches of them, even when not leading 
to disaster. The most perfect steering rules cannot 
but leave a margin of doubt in the limit between 
the two cases in which a ship ought to alter its 
course and ought not to do so, or again between the 
two cases in which a ship ought to alter its course 
in one direction, and ought to alter its course in 
the contrary direction. This doubt essentially 

1 By "rule of the road," I did not mean to include the rules con- 
cerning lights to be carried by ships or boats at sea which form part 
of the whole set of " Regulations for Preventing Collisions at Sea." 
These rules too are generally approved of, but in some important 
details various amendments have been urged on very good grounds. 


involves risk of collision, which can only be 
obviated by fulfilment of the first clause of 
Art. 1 6. "Every steam ship, when approaching 
another ship so as to involve risk of collision, 
shall slacken her speed, or, if necessary, stop and 
reverse." It is not too much to say that no 
collision between two steamers, or between a 
steamer and a sailing ship, ever occurred in 
daylight, and in clear and moderate weather, 
which could not have been avoided by the timely 
observance of this rule by at least one of the two 

64. Art. 10 of the Regulations which I have read 
to you leads me to speak of the fog-horn, of which, 
through the kindness of Mr. N. Holmes, I am able 
to show you some very excellent specimens this 
evening. You hear how loud even the smallest 
of them is. 

The question how far a sound can be heard at 
sea is a very difficult one, and involves some 
exceedingly subtle principles regarding the pro- 
perties of matter and problems of abstract 
dynamics. In a paper by Professor Henry in 


the 1874 Report of the United States Lighthouse 
Board, in official papers printed by the House 
of Commons in 1874 and 1875, and in the recent 
edition of Tyndall's Lectures on Sound, very 
interesting and important results of observations 
are described, showing that in certain states of 
the atmosphere (which seem to depend on a 
streaky distribution of density, due to the com- 
mingling of warmer and colder air, or as suggested 
by Professor Osborne Reynolds, on an upward 
curvature of the lines of propagation of sound 
due to colder air above than below, or on both 
causes combined) sound ceases to be heard at 
extraordinarily small distances. One thing 
brought out by these investigations is, that a 
fog, however dense, is by no means unfavourable 
to the transmission of sound, and that it is often 
in clear bright days that sound travels worst. 

65. In respect to navigation, it is satisfactory to 
know that in the densest fog, with moderate weather 
(and dense fogs generally occur only in moderate 
weather), a sailing ship or steamer, sufficiently and 
judiciously using a fog-horn, such as the most 


powerful of those you have now seen and heard, 
or a good steam whistle, can, if not going at a 
speed of more than four or five knots, give ample 
warning of her approach, and sufficient indication 
of her position, to allow any other vessel to give 
similar information in return, in good time for the 
two, if both acting judiciously, to surely avoid 
collision by daylight. It is almost a pleasure to 
be in the British or Irish Channel by daylight in 
a dense fog, and to perceive so vividly through 
your ears that you imagine you see a steamer 
sounding her steam whistle and crossing your bow 
at a safe distance, or a sailing vessel coming down 
free on your starboard quarter, when you are 
creeping to windward on the starboard tack. The 
pleasure, such as it is, is no doubt greatly marred 
by the thought that there may be near you some 
lubber, or as I should prefer to say, felon, whether 
under steam or canvas, sounding neither steam 
whistle nor fog-horn. 

I am informed by Mr. Thomas Gray, of the 
Board of Trade, that probably soon a great im- 
provement is to be made in the system of fog 


signals, by providing that every vessel shall not 
merely sound her steam whistle or fog-horn, but 
shall do so according to a carefully arranged code 
of signals, so as to give certain definite useful in- 
formation as to any change of course she (if a 
steamer) may be making or be on the point of 
making, and (if a sailing ship) so as to show the 
tack on which she is sailing. 

66. This brings me, almost in conclusion, to 
speak of the communication of information, or 
orders from ship to ship, by signals. The methods 
chiefly used are : 

(1) Signalling by flags. This, when worked by 
very skilful signalmen, as in the Royal Navy, is the 
most effective method at present in use for signal- 
ling by day from ship to ship in clear weather. 

(2) For signalling in clear weather by night, 
Captain Colomb's method by short and long flashes 
has been successfully used in the British Navy for, 
I believe, nearly twenty years. It has also been 
largely used on land by our army, as in the 
Abyssinian war. It is curious to find in military 
operations of the nineteenth century a return to a 


kind of telegraph due, it seems, originally to 
Aeneas, a Greek writer on tactics, and improved 
by Polybius. 1 The essential characteristic of 
Captain Colomb's method, on which its great 
success has depended, consists in the adoption of 
the Morse system of telegraphing by rapid suc- 
cession of shorts and longs, " dots " and " dashes " 
as they are called ; and, I believe, its success would 
have been still greater, certainly its practice would 
have been by the present time much more familiar 
to every officer and man in the service than it is 
now, had not only the general principle of the Morse 
system but the actual Morse alphabet for letters 
and numerals been adopted by Captain Colomb. 
A modification of Captain Colomb's system, which 
many practical trials has convinced me is a great 
improvement, consists in the substitution of short 
and long eclipses for short and long flashes, except 
when his magnesium lamp is to be used, as it is 
when, whether from the greatness of the distance 
to which the signals are to be sent, or from 

1 Polybius, X. 44. Or see Rollin's Ancient History, Book 
XVIII., Sec. 6. 


the state of the atmosphere, the light of a power- 
ful oil lamp is insufficient. In the system of short 
and long eclipses, the signal lamp is allowed 
to show its light uninterruptedly until the signal 
commences. Then groups of long and short 
eclipses the short eclipses of about half a second's 
duration, the long eclipses three half seconds, the 
interval or intervals of brightness between the 
eclipses of a group half a second ; such groups, I 
say, of long and short eclipses are produced by a 
movable screen, worked by the sender of the 
message, and read off as letters, numerals, or code 
signals by the receiver or receivers. Experience 
shows that a person, familiar with the flash method, 
can, without further practice, read off the eclipses 
with equal ease, and vice versa ; and, when it is ad- 
visable to use the magnesium lamp, both sender and 
receivers will be equally quick and sure in their use 
of it if they ordinarily use the eclipse method instead 
of, as now in the navy, the method of long and short 
flashes. Whenever the light of a lamp suffices, 
the eclipse method is decidedly surer, particularly 
at quick speeds of working, than the flash method, 


and it has besides the great advantage of showing 
the receivers exactly where to look for the signals 
when they come, by keeping the signal lamp 
always in view in the intervals between signals, 
instead of keeping it eclipsed in the intervals as in 
Colomb's method. 

(3) Colomb's method of shorts and longs has 
also been practised, with great success, in fogs by 
day and by night, with long and short blasts of 
the steam whistle or fog-horn, instead of long 
and short flashes of light. 

67. But here again a very great improvement is 
to be made. Use instead of the distinction between 
short and long the distinction between sounds of 
two different pitches, the higher for the " dot," the 
lower for the "dash." Whether in the steam 
whistle or the fog-horn a very sharp limitation 
of the duration of the signal is scarcely attain- 
able. There is, in fact, an indecision in the 
beginning and end of the sound, which renders 
quick and sure Morse signalling by longs and 
shorts impracticable, and entails a painful slow- 
ness, and a want of perfect sureness, especially 


when the sound is barely audible. Two fog-horns 
or two steam whistles, tuned to two different notes, 
or when the distance is not too great, two notes 
of a bugle or cornet may be used to telegraph 
words and sentences with admirable smartness and 
sureness. Five words a minute are easily attain- 
able. Let any reader take the trouble to commit 
to memory the annexed Morse alphabet. He will 
know it all by heart in a day, and then w r ith a little 
practice, he w r ill soon be able to speak by two 
notes of a pianoforte, or -two notes of his voice 
or by whistling two notes with his lips, at the rate 
of eight or ten w r ords per minute. This method 
has the great advantage that, if the sounds can be 
heard at all, the distinction between the higher 
and the lower, or as we may say for brevity, 
" acute " and " grave," is unmistakable : whereas 
the distinction between long and short blasts is 
lost, or becomes uncertain, long before the sound is 

VOL. III. K - 



I. Short and long electric marks, or short and 
long eclipses of a lamp, or short and long flashes 
of light, or short and long blasts of sound. 

II. Movements of one or other of two objects 

(as left and right hand). 
Movements to left and right, 
Or movements upwards and downwards. 

III. Two sounds of different musical notes 
acute and grave. 

Short. f Long. 

Left. J Right. 

Upward movement. j Downward movement. 

Acute sound. ( Grave. 

Understand ABCDEFGH 

T U V W X Y Z Understand. 

7890 Understand. 


68. An old instrument called the siren, in- 
vented by Cagniard de la Tour, for the purpose 
of illustrating the science of sound, has been 
recently taken up by the United States Light- 
house Board with great success, as a sub- 
stitute for the fog horns previously used at 
lighthouses in foggy weather. The siren, in 
its original form, is an instrument in which a 
hole or holes in a flat side or top of an air 
vessel, are alternately obstructed and opened by 
the revolution of a disc of metal, perforated 
with a number of equidistant holes in a circle 
round its axis. Air blown constantly into the 
vessel escapes alternately in abundance, and 
but slightly, as the holes are alternately opened 
and obstructed by the revolution of the disc ; and 
thus a musical note is produced, with a pitch 
precisely determined by the number of openings 
and closings per second of time. Instead of a 
little instrument, suitable for a lecture-room table, 
both turned and having its blast supplied by a 
small acoustic wind-chest and bellows, the 
Americans have made a powerful instrument with 

K 2 


large disc, driven at a uniform l rate by wheelwork, 
and the blast supplied from a steam boiler, or from 
a large vessel of compressed air, sustained by 
powerful condensing pumps. I am informed that 
recently an improvement has been made in this 
country by substituting a rotating cylinder for the 
rotating disc. 

69. Professor's Henry's experiment made for 
the United States Lighthouse Board, of which 
he is chairman, showed that the siren was much 
superior to the powerful fog-horns and steam 

1 It seems that improvement in respect to this quality is needed 
in the instruments hitherto made. In some of the reports of the 
experiments, I see it stated that the pitch of the sound gradually 
fell when the siren was kept sounding continuously for some time ; 
because the steam pressure in the boiler diminished, and so the 
rotating disc ran slower. The rotating disc ought to be kept running 
with almost chronometric uniformity. There is not the slightest 
difficulty in doing this by having it driven either by a constant 
weight, or by aid of a proper slip gear adapted to drive with con- 
stant force. With this and a proper centrifugal governor, there is 
no difficulty whatever in securing so nearly perfect uniformity that 
the rate shall never alter by as much as I per cent. This would 
produce not more than 1/4 of a semitone of difference in the pitch of 
the note. The power required to turn the disc is so very moderate 
that there is absolutely no difficulty in realising the improvement I 
have now suggested. Possibly the best plan will be to drive it by 
manual power. One man amply suffices for the purpose. 


whistles which had previously been in use at 
their lighthouses ; and in a series of investigations 
on the transmission of sound, under the auspices 
of the English Trinity House, with a siren lent 
for the purpose by the United States Lighthouse 
Board, Professor Tyndall arrived at the same 
conclusion, and found that often, and especially 
in the more difficult circumstances, the siren 
surpasses a signal gun in audibility at a distance. 
There being, at all events, no doubt of its constant 
superiority over fog-horns and steam whistles, it 
seems that it ought immediately to be substituted 
for them in our navy as means for communicating 
intelligence, and giving orders from ship to ship 
in a fog. Introduced for use in fogs, it will pro- 
bably soon, in clear weather, supplant flags by 
day and lamps by night, for much of the ordinary 
telegraphic work between ships of war when at 
sea. One thing stands out most clear from 
the evidence produced at the recent court-martial 
regarding the loss of the Vanguard, and that is 
that great improvement in this respect is urgently 
needed. Short and long blasts of the siren 


might be advantageously substituted for short 
and long blasts of the steam whistle, but much 
more advantageously short blasts of two sirens on 
the same shaft, or on two shafts geared together, 
sounding different notes, acute note for the short, 
grave note for the long. 

70. HOLMES' RESCUE LIGHT. I shall conclude 
by bringing before you (Fig. 16) an invention of a 
most beneficent character. It is a light for life- 
buoys, invented by Mr. Nathaniel Holmes, and 

FIG. 16. 

depending on the well-known property of phos- 
phuretted hydrogen, to take fire when it bubbles 
up from water. It is, I believe, contemplated by 


the Board of Trade to make a rule requiring that 
every British ship going to sea shall be provided 
with this adjunct to the life buoys, a most proper 
requirement as seems to me. Even in the best 
found and best disciplined ships the accident 
does sometimes happen of a man overboard. 
The life-buoy is thrown, but in the dark the man 
may not see it, or if he does see it and reach 
it, and keep himself afloat by it, the people in 
the ship, as she runs on, lose sight of him before 
she can be brought to and a boat lowered. Till 
now, I believe, it may be said that not once in 
a hundred times is a man rescued who falls over- 
board in a dark night from a large ship sailing 
or steaming rapidly through the water. 

71. But if a life-buoy is thrown, with one of 
these rescue lights attached to it, as I now throw 
it, you see what happens. You see this metal 
vessel full of phosphuret of calcium. 1 It is lashed 

1 I am indebted to Mr. Nathaniel Holmes for the following de- 
scription of the construction of his patent Rescue Light : " I take 
" lumps of common chalk broken in pieces about the size of lump- 
" sugar, these are placed in a crucible with certain proportions of 
" prepared phosphorus, and the whole is placed in a furnace, and 


strongly to the life-buoy so that neither can be 
thrown into the water without the other. I must 
not forget to pluck away these soft solder stoppers 
from the conical end below, and the top of the 
projecting tube above. Having done so, I now 
throw both the life-buoy and rescue light over- 
board. All this is done within ten seconds of 
time, after I hear the alarm " a man overboard." 
You see now the moment the metal vessel plunges 
into the water, it begins to smoke vehemently, and 
almost instantly flames rise (Fig. 17). The man in 
the water sees the light, swims towards it, catches 
the life-bouy, and supports himself securely by 
it. No danger now of him sinking or being 

' * heated to a certain degree over cherry red. The phosphorus, by 
' ' the heat, is converted into vapour, and the red-hot chalk takes up 
" this vapour to saturation." "When cooled, the contents, phos- 
" phuret of calcium and phosphate of calcium " (the former the 
active ingredient), "are placed in the tin cases and soldered down. 
"Upon using the signal, the water is admitted, and " acting on the 
phosphuret of calcium, produces " phosphuretted hydrogen, which 
" issuing out of the upper orifice, catches fire spontaneously, and 
bursts into flame." 

1 " The process of manufacture shows that the rescue signals 
" are free from danger, are not affected by either heat, friction, or 
" percussion, water alone can ignite them." 



drowned by the water washing over him, or by 
his getting his head under water. It is solely a 

FIG. 17. 

question of the water's temperature, and of his 
own vigour, how long he may live. Already the 
ship, dashing along at fourteen knots, is a quarter 


of a mile off, and before a boat can be manned 
and cast off from her, she must be at least half 
a mile from the life-buoy with its living burden. 
But look at the light the more the water washes 
over it, the more brightly it burns. It will burn 
for three-quarters of an hour, and can be seen 
at a distance of five or six miles. It disappears 
for a few seconds perhaps behind a wave, or 
for the want of continuity which you see in the 
flame, and then you see it blaze up again with 
increased brilliance, and so on for three-quarters of 
an hour. It goes on disappearing and blazing 
up again visibly out of the horizon when at least 
five or six miles off, as I have myself seen in the 
river Para. The boat, now manned and rowing 
away from the ship, has no difficulty in knowing 
where to steer for. Guided by the light, they 
will pull away through a heavy sea, and in 
a quarter of an hour they have their comrade 
in the boat with them. By this time the ship, 
also guided by the light, has steamed or sailed 
close up to them, and in a few minutes they 
are all on board. 


[Evening Lecture to the British Association at the South- 
ampton Meeting, Friday ', August 25, 1882.] 

THE subject on which I have to speak this evening 
is the Tides, and at the outset I feel in a curiously 
difficult position. If I were asked to tell what 
I mean by the Tides I should feel it exceedingly 
difficult to answer the question. The tides have 
something to do with motion of the sea. Rise 
and fall of the sea is sometimes called a tide ; but 
I see, in the Admiralty Chart of the Firth of 
Clyde, the whole space between Ailsa Craig and 
the Ayrshire coast marked "very little tide here." 
Now, we find there a good ten feet rise and fall, 
and yet we are authoritatively told there is very 
little tide. The truth is, the word " tide " as used 


by sailors at sea means horizontal motion of the 
water ; but when used by landsmen or sailors in 
port, it means vertical motion of the water. I hope 
my friend Sir Frederick Evans will allow me to 
say that we must take the designation in the chart, 
to which I have referred, as limited to the instruc- 
tion of sailors navigating that part of the sea, and 
to say that there is a very considerable landsman's 
tide there a rise and fall of the surface of the 
water relatively to the land though there is 
exceedingly little current. 

One of the most interesting points of tidal theory 
is the determination of the currents by which the 
rise and fall is produced, and so far the sailor's idea 
of what is most noteworthy as to tidal motion is 
correct : because before there can be a rise and fall 
of the water anywhere it must come from some 
other place, and the water cannot pass from place 
to place without moving horizontally, or nearly 
horizontally, through a great distance. Thus the 
primary phenomenon of the tides is after all the 
tidal current ; and it is the tidal currents that are 
referred to on charts where we have arrow-heads 


marked with the statement that we have " very 
little tide here," or that we have " strong tides " 

One instance of great interest is near Portland. 
\Ye hear of the " race of Portland " which is pro- 
duced by an exceedingly strong tidal current ; but 
in Portland harbour there is exceedingly little rise 
and fall, and that little is much confused, as if the 
water did not know which way it was going to 
move. Sometimes the water rises, sinks, seems to 
think a little while about it, and then rises again. 
The rise of the tide at Portland is interesting to 
the inhabitants of Southampton in this, that 
whereas here, at Southampton, there is a double 
high water, there, at Portland, there is a double 
low water. The double high water seems to 
extend across the Channel. At Havre, and on 
the bar off the entrance to Havre, there is a 
double high water very useful to navigation ; but 
Southampton I believe is pre-eminent above all 
the ports in the British Islands with respect to 
this convenience. There is here (at Southampton) 
a good three hours of high water ; a little dip 


after the first high water, and then the water 
rises again a very little more for an hour and a 
half or two hours, before it begins to fall to low 

I shall endeavour to refer to this subject again. 
It is not merely the Isle of Wight that gives rise 
to the phenomenon. The influence extends to 
the east as far as Christchurch, and is reversed at 
Portland, and we have the double or the prolonged 
high water also over at Havre ; therefore, it is 
clearly not, as it has been supposed to be, due to 
the Isle of Wight. 

But now I must come back to the question 
What are the " Tides " ? Is a " tidal wave " a 
tide ? What is called in the newspapers a " tidal 
wave " rises sometimes in a few minutes, does great 
destruction, and goes down again, somewhat less 
rapidly. There are frequent instances in all parts 
of the world of the occurrence of that phenomenon. 
Such motions of the water, however, are not tides ; 
they are usually caused by earthquakes. But \ve 
are apt to call any not very short-time rise and 
fall of the water a tide, as when standing on the 


coast of a slanting shore where there are long 
ocean waves, we see the gradual sinkings and 
risings produced by them, and say that it is a 
wave we see, not a tide, till one comes which is ex- 
ceptionally slow, and then we say " that is liker a 
tide than a wave." The fact is, there is something 
perfectly continuous in the species of motion called 
wave, from the smallest ripple in a musical glass, 
whose period may be a thousandth of a second 
to a " lop of water " in the Solent, whose period is 
one or two seconds, and thence on to the great 
ocean wave with a period of from fifteen to twenty 
seconds, where ends the phenomenon which we 
commonly call waves (Fig. 18, p. 144), and not tides. 
But any rise and fall which is manifestly of longer 
period, or slower in its rise from lowest to highest, 
than a wind wave, w r e are apt to call a tide ; and 
some of the phenomena that are analysed for, and 
worked out in this very tidal analysis that I am 
going to explain, are in point of fact more 
properly wind waves than true tides. 

Leaving these complicated questions, however, 
I will make a short cut, and assuming the cause 


without proving it, define the thing by the cause. 
I shall therefore define tides thus : Tides are 
motions of water on the earth, due to the attrac- 
tions of the sun and of the moon. I cannot say 
tides are motions due to the actions of the sun and 
of the moon ; for so I would include, under the 
designation of tide, every ripple that stirs a puddle 
or a millpond, and waves in the Solent or in the 

FIG. 1 8. Wave forms. 

English Channel, and the long Atlantic wind 
waves, and the great swell of the ocean from one 
hemisphere to the other and back again (under 
the name which I find in the harmonic reduction 
of tidal observations), proved to take place once a 
year, and which I can only explain as the result 
of the sun's heat. 

But while the action of the sun's heat by means 


of the wind produces ripples and waves of every 
size, it also produces a heaping-up of the water 
as illustrated by this diagram (Fig. 19). Suppose 
we have wind blowing across one side of a sheet 
of water, the wind ruffles the surface, the waves 
break if the wind is strong, and the result is a 
strong tangential force exerted by the wind on 
the surface water. If a ship is sailing over the 

FIG. 19. Showing the heaping-up of water produced by wind. 

water there is strong tangential force ; thus the 
water is found going fast to leeward for a long 
distance astern of a great ship sailing with a side 
wind : and, just as the sails of a ship standing 
high above the sea give a large area for the wind 
to act upon, every wave standing up gives a 
surface, and we have horizontal tangential force 
over the whole surface of a troubled sea. The 
VOL. ill. L 


result is that water is dragged along the surface 
from one side of the ocean to the other from 
one side of the Atlantic to the other and is 
heaped up on the side towards which the wind is 
blowing. To understand the dynamics of this 
phenomenon, think of a long straight canal with 
the wind blowing lengthwise along it. In virtue 
of the tangential force exerted on the surface of 
the water by the wind, and which increases with 
the speed of the wind, the water will become 
heaped up at one end of the canal, as shown in 
the diagram (Fig. 19), while the surface water 
throughout the whole length will be observed 
moving in the direction of the wind say in the 
direction of the two arrows near to the surface of 
the water above and below it. But to re-establish 
the disturbed hydrostatic equilibrium, the water 
so heaped up will tend to flow back to the end 
from which it has been displaced, and as the wind 
prevents this taking place by a surface current, 
there will be set up a return current along the 
bottom of the canal, in a direction opposite to 
that of the wind, as indicated by the lowermost 


arrow in the diagram (Fig. 19). The return current 
in the ocean, however, is not always an under 
current, such as I have indicated in the diagram, 
but may sometimes be a lateral current. Thus a 
gale of wind blowing over ten degrees of latitude 
will cause a drag of water at the surface, but the 
return current may be not an under current but a 
current on one side or the other of the area affected 
by the wind. Suppose, for instance, in the 
Mediterranean there is a strong east wind blowing 
along the African coast, the result will be a current 
from east to wes f along that coast, and a return 
current along the northern coasts of the 

The rise and fall of the water due to these 
motions are almost inextricably mixed up with 
the true tidal rise and fall. 

There is another rise and fall, also connected 
with the heating effect of the sun, that I do not 
call a true tide, and that is a rise and fall due to 
change of atmospheric pressure. When the 
barometer is high over a large area of ocean, then, 
there and in neighbouring places, the tendency to 

L 2 


hydrostatic equilibrium causes the surface of the 
water to be lower, where it is pushed down by the 
greater weight of air, and to be higher where there 
is less weight over it. It does not follow that in 
every case it is lower, because there may not be 
time to produce the effect, but there is this tendency. 
It is very well known that two or three days of low 
barometer make higher tides on our coast. In 
Scotland and England and Ireland, two or three 
days of low barometer generally produce all round 
the shore higher water than when the barometer is 
high ; and this effect is chiefly noticed at the time 
of tidal high water, because people take less 
notice of low water as at Portland where they 
think nothing of the double low water. Hence 
we hear continually of very high tides very 
high water noticed at the time of high tides 
when the barometer is low. We have not 
always, however, in this effect of barometric 
pressure really great tidal rise and fall. On the 
contrary we have the curious phenomenon that 
sometimes when the barometer is very low, and 
there are gales in the neighbourhood, there is very 


little rise and fa!!, as the water is kept heaped up 
and does not sink by anything like its usual amount 
from the extra high level that it has at high water. 
But I fear I have got into questions which are 
leading me away from my subject, and as I 
cannot get through them I must just turn back. 

Now think of the definition which I gave of the 
"tides," and think of the sun alone. The action of 
the sun cannot be defined as the cause of the solar 
tides. Solar tides are due to action of the sun, but 
all risings and fallings of the water due to the action 
of the sun are net tides. We want the quantifica- 
tion of the predicate here very badly. We have a 
true tide depending on the sun, the mean solar 
diurnal tide, having for its period twenty-four solar 
hours, which is inextricably mixed up with those 
meteorological tides that I have just been speaking 
of tides depending on the sun's heat, and on the 
variation of the direction of the wind, and on the 
variation of barometric pressure according to the 
time of day. The consequence is that in tidal 
analysis, when we come to the solar tides, we can- 
not know how much of the analysed result is due 


to attraction, and how much to heating effect 
directly or indirectly, whether on water, or on air, 
or on water as affected by air. As to the lunar 
tides we are quite sure of them ; they are gravita- 
tional, and nothing but gravitational ; but I hope 
to speak later of the supposed relation of the moon 
to the weather, and the relation that has to the 

I have defined the tides as motions of water on 
the earth due to the attractions of the sun and of 
the moon. How are we to find out whether an 
observed motion of the water is a tide or is not a 
tide as thus defined ? Only by the combination of 
theory and observation : if these afford sufficient 
reason for believing that the motion is due to 
attraction of the sun or of the moon, or of both, 
then we must call it a tide. 

It is curious to look back on the knowledge of 
the tides possessed in ancient times, and to find as 
early as two hundred years before the Christian era 
a very clear account given of the tides at Cadiz. 
But the Romans generally, knowing only the 
Mediterranean, had not much clear knowledge of 


the tides. At a much later time than that, we hear 
from the ancient Greek writers and explorers 
Posidonius, Strabo, and others that in certain 
remote parts of the world, in Thule, in Britain, in 
Gaul, and on the distant coasts of Spain, there 
were motions of the sea a rising and falling of the 
water which depended in some way on the moon. 
Julius Caesar came to know something about it ; but 
it is certain the Roman Admiralty did not supply 
Julius Caesar's captains with tide tables when he 
sailed from the Mediterranean with his expedition- 
ary force, destined to put down anarchy in Britain. 
He says, referring to the fourth day after his first 
landing in Britain " That night it happened to be 
full moon, which time is accustomed to give the 
greatest risings of water in the ocean, though our 
people did not know it." It has been supposed 
however that some of his people did know it some 
of his quartermasters had been in England before 
and did know but that the discipline in the 
Roman navy was so good that they had no right 
to obtrude their knowledge ; and so, although a 
storm was raging at the time, he was not told that 


the water would rise in the night higher than usual, 
and nothing was done to make his transports 
secure higher up on the shore while he was 
fighting the Britons. After the accident Csesar 
was no doubt told " Oh, we knew that before, 
but it might have been ill taken if we had 
said so." 

Strabo says "Soon after moonrise the sea 
begins to swell up and flow over the earth till the 
moon reaches mid heaven. As she descends thence 
the sea recedes till about moonset, when the water 
is lowest. It then rises again as the moon, below 
the horizon, sinks to mid heaven under the earth." 
It is interesting here to find the tides described 
simply with reference to the moon. But there is 
something more in this ancient account of Strabo ; 
he says, quoting Posidonius " This is the daily 
circuit of the sea. Moreover, there is a regular 
monthly course, according to which the greatest 
rise and fall takes place about new moon, then 
diminishing rise and fall till half moon, and again 
increasing till full moon." And lastly he refers to 
a hearsay report of the Gaditani (Cadizians) regard- 


ing an annual period in the amount of the daily 
rise and fall of the sea, which seems to be not 
altogether right, and is confessedly in part con- 
jectural. He gave no theory, of course, and he 
avoided the complication of referring to the sun. 
But the mere mention of an annual period is 
interesting in the history of tidal theory, as sug- 
gesting that the rises and falls are due not to the 
moon alone but to the sun also. The account 
given by Posidonius is fairly descriptive of what 
occurs at the present day at Cadiz. Exactly the 
opposite would be true at many places ; but at 
Cadiz the time of high water at new and full moon 
is nearly twelve o'clock. Still, I say we have only 
definition to keep us clear of ambiguities and 
errors ; and yet, to say that those motions of the 
sea which we call tides depend on the moon, was 
considered, even by Galileo, to be a lamentable 
piece of mysticism which he read with regret 
in the writings of so renowned an author as 

It is indeed impossible to avoid theorising. The 
first who gave a theory was Newton ; and I shall 


now attempt to speak of it sufficiently to allow us 
to have it as a foundation for estimating the forces 
with which we are concerned, in dealing with some 
of the very perplexing questions which tidal 
phenomena present. 

We are to imagine the moon as attracting the 
earth, subject to the forces that the different bodies 
exert upon each other. We are not to take Hegel's 
theory that the Earth and the Planets do not 
move like stones, but move along like blessed gods, 
each an independent being. If Hegel had any 
grain of philosophy in his ideas of the solar system, 
Newton is all wrong in his theory of the tides. 
Newton considered the attraction of the sun upon 
the earth and the moon, of the earth upon the 
moon, and the mutual attractions of different parts 
of the earth ; and left it for Cavendish to complete 
the discovery of gravitation, by exhibiting the 
mutual attraction of two pieces of lead in his 
balance. Tidal theory is one strong link in the 
grand philosophic chain of the Newtonian theory 
of gravitation. In explaining the tide-generating 
force we are brought face to face with some of the 


subtleties, and with some of the mere elements, of 
physical astronomy. I will not enter into details, 
as it would be useless for those who already 
understand the tidal theory, and unintelligible to 
those who do not. 

I may just say that the moon attracts a piece of 
matter, for example a pound-weight, here on the 
earth, with a force which we compare with the 
earth's attraction thus. Her mass is 1/80 of the 
earth's, and she is sixty times as far away from the 
earth's centre as we are here. Newton's theory 
of gravitation shows, that when you get outside 
the mass of the earth the resultant attraction of 
the earth on the pound weight, is the same as if 
the whole mass of the earth were collected at 
the centre, and that it varies inversely as the 
square of the distance from the centre. The same 
law is inferred regarding the moon's attraction 

from the general theory. The moon's attraction 


on this pound weight is therefore 8 , or 


288000 ^ ^ e at ti"action f tne earth on the 
same mass. But that is not the tide-generating 


force. The moon attracts any mass at the nearest 
parts of the earth's surface with greater force than 
an equal mass near the centre ; and attracts a mass 
belonging to the remoter parts with less force. 
Imagine a point where the moon is overhead, and 
imagine another point on the surface of the earth 
at the other end of a diameter passing through the 
first point and the centre of the earth (illustrated 
by B and A of Fig. 20, p. 161). The moon attracts 
the nearest point (B) with a force which is greater 
than that with which it attracts the farther point (A) 
in the ratio of the square of 59 to the square of 61. 
Hence the moon's attraction on equal masses at the 
nearest and farthest points differs by one fifteenth 
part of her attraction on an equal mass at the 
earth's centre, or about a 4,32O,oooth, or, roughly, a 
four-millionth, of the earth's attraction on an equal 
mass at its surface. Consequently the water tends 
to protrude towards the moon and from the moon. 
If the moon and earth were held together by a rigid 
bar the water would be drawn to the side nearest 
to the moon drawn to a prodigious height of 
several hundred feet. But the earth and moon are 


not so connected. We may imagine the earth as 
falling towards the moon, and the moon as falling 
towards the earth, but never coming nearer ; the 
bodies, in reality, revolving round their common 
centre of gravity. A point nearest to the moon is as 
it were dragged away from the earth, and thus the 
result is that apparent gravity differs by about one 
four-millionth at the points nearest to and farthest 
from the moon. At the intermediate points of 
the circle C, D (Fig. 20, p. 161), there is a somewhat 
complicated action according to which gravitation 
is increased by about one I /-millionth, and its 
direction altered by about one I /-millionth, so that 
a pendulum 17,000 feet long, a plummet rather 
longer than from the top of Mont Blanc to sea level, 
would, if showing truly the lunar disturbing force, 
be deflected through a space of one thousandth of 
a foot. It seems quite hopeless by a plummet to 
exhibit the lunar disturbance of gravity. A spring 
balance to show the alteration of magnitude, and 
a plummet to show the change of direction are 
conceivable ; but we can scarcely believe that 
either can ever be produced, with sufficient deli- 


cacy and consistency and accuracy to indicate 
these results. 

A most earnest and persevering effort has been 
made by Mr. George Darwin and Mr. Horace 
Darwin to detect variations in gravity due to lunar 
disturbance, and they have made apparatus which 
notwithstanding the prodigious smallness of the 
effect to be observed, is in point of delicacy and 
consistency capable of showing it ; but when they 
had got their delicate pendulum their delicate 
plummet about the length of an ordinary seconds' 
pendulum and their delicate multiplying gear to 
multiply the motion of its lower end by about a 
million times, and to show the result on a scale 
by the reflection of a ray of light, they found 
the little image incessantly moving backward and 
forward on the scale with no consistency or regu- 
larity ; and they have come to the conclusion 
that there are continual local variations of ap- 
parent gravity taking place for which we know 
no rule, and which are considerably greater than 
the lunar disturbance for which they were seeking. 
That which they found continual motions of the 


surface of the earth, and which was not the 
primary object of their investigation is in some 
respects more interesting than what they sought 
and did not find. The delicate investigation thus 
opened up promises a rich harvest of knowledge. 
These disturbances are connected with earthquakes 
such as have been observed in a very scientific 
and accurate manner by Milne, Thomas Gray, 
and Ewing in Japan, and in Italy by many 
accurate observers. All such observations agree 
in showing continual tremor and palpitation of 
the earth in every pnrt. 

One other phenomenon that I may just refer 
to now as coming out from tide-guage observa- 
tions, is a phenomenon called seiches by Forel, 
and described by him as having been observed 
in the lakes of Geneva and Constance. He 
attributes them to differences of barometric 
pressure at the ends of the lake, and it is pro- 
bable that part of the phenomenon is due to 
such differences. I think it is certain, however, 
that the whole is not due to such differences. 
The Portland tide curve and those of many other 


places, notably the tide curve for Malta, taken 
about ten years ago by Sir Cooper Key, and 
observations on the Atlantic coasts and in many 
other parts of the world, show something of 
these phenomena ; a ripple or roughness on the 
curve traced by the tide gauge, which, when 
carefully looked to, indicates a variation not 
regular but in some such period as twenty or 
twenty-five minutes. It has been suggested that 
they are caused by electric action ! Whenever 
the cause of a thing is not known it is immediately 
put down as electrical ! 

. I would like to explain to you the equilibrium 
theory, and the kinetic theory, of the tides, but 
I am afraid I must merely say there are such 
things ; and that Laplace in his great work, his 
Mecanique Celeste, first showed that the equi- 
librium theory was utterly insufficient to account 
for the phenomena, and gave the true principles 
of the dynamic action on which they depend. 
The resultant effect of the tide-generating force 
is to cause the water to tend to become protube- 
rant towards the moon and the sun and from 



them, when they are in the same straight line, 
and to take a regular spheroidal form, in which 
the difference between the greatest and the least 
semi-diameter is about 2 feet for lunar action alone, 
and i foot for the action of the sun alone that 

FIG. 20. Spring Tides. 

FIG. 21. Spring Tides. 

is a tide which amounts to 3 feet when the sun and 
moon act together (Figs. 20 and 21), and to I foot 
only when they act at cross purposes (Figs. 22 
and 23), so as to produce opposite effects. These 
diagrams, Figs. 20 to 23, illustrate spring and neap 
tides : the dark shading around the globe, E, repre- 


FIG. 22. Neap Tides. 

FIG. 23. Neap Tides. 


senting a water envelope surrounding- the earth. 
There has been much discussion on the origin 
of the word neap. It seems to be an Anglo-Saxon 
word meaning scanty. Spring seems to be the 
same as when we speak of plants springing up. 
I well remember at the meeting of the British 
Association at Edinburgh a French member who, 
meaning spring tides, spoke of the grandes marees 
die printemps. Now you laugh at this ; and yet, 
though he did not mean it, he was quite right, 
for the spring tides in the spring time are greater 
on the whole than those at other times, and we 
have the greatest spring tides in the spring of 
the year. But there the analogy ceases, for we 
have also very high spring tides in autumn. Still 
the meaning of the two words is the same etymo- 
logically. Neap tides are scanty tides, and spring 
tides are tides which spring up to remarkably 
great heights. 

The equilibrium theory of the tides is a way 
of putting tidal phenomena. We say the tides 
would be so and so if the water took the figure 
of equilibrium. Now the water does not cover 

M 2 


the whole earth, as we have assumed in the dia- 
grams (Figs. 48 to 5 1 ), but the surface of the water 
may be imagined as taking the same figure, so 
far as there is water, that it would take if there 
were water over the whole surface of the earth. 
But here a difficult question comes in namely, 
the attraction of the water for parts of itself. 
If we consider the water flowing over the whole 
earth this attraction must be taken into account. 
If we imagine the water of exceedingly small 
density so that its attraction on itself is insensible 
compared with that of the earth, we have thus 
to think of the equilibrium theory. But, on the 
other hand, if the water had the same density 
as the earth, the result would be that the solid 
nucleus would be almost ready to float ; and 
now imagine that the water is denser than the 
earth, and we put the tides out of consideration 
altogether. Think of the earth covered over with 
mercury instead of water a layer of mercury a 
foot deep. The solid earth would tend to float, 
and would float, and the result would be that 
the denser liquid would run to, and cover one 


side up to a certain depth, and the earth would 
be as it were floating out of the sea. That ex- 
plains one curious result that Laplace seems to 
have been much struck with : the stability of 
the ocean requires that the density of the water 
should be less than that of the solid earth. But 
take the sea as having the specific gravity of 
water, the mean density of the earth is only 
5 "6 times that of water, and this is not enough 
to prevent the attraction of water for water from 
being sensible. Owing therefore to the attraction 
of the water for parts of itself the tidal pheno- 
mena are somewhat larger than they would be 
without it, but neglecting this, and neglecting 
the deformation of the solid earth, we have the 
ordinary equilibrium theory. 

Why does the water not follow the equilibrium 
theory ? Why have we tides of 20 feet or 30 
feet or 40 feet in some places, arid only of 2 or 
3 feet in others ? Because the water has not 
time in the course of 12 hours to take the equi- 
librium figure, and because after tending towards 
it, the water runs beyond it. 


I ask you to think of the oscillations of water 
in a trough. Look at this diagram (Fig. 24), which 
will help you to understand how the tidal effect 
is prodigiously magnified by a dynamical action 
due to the inertia of the water. The tendency 
of water in motion to keep its motion prevents 
it from taking the figure of equilibrium. [A 

FIG. 24. Oscillations of Water in a Trough. 

chart showing the tides of the English Channel 
was exhibited, from which it was seen that while 
at Dover there were tides of 21 feet, there was 
at Portland very little rise and fall.] Imagine a 
canal instead of the English Channel, a canal 
stopped at the Straits of Dover and at the 


opposite end at Land's End, and imagine some- 
how a disturbing force causing the water to be 
heaped up at one end. There would be a swing 
of water from one end to the other, and if the 
period of the disturbing force approximately 
agreed with the period of free oscillation, the 
effect would be that the rise and fall would go 
vastly above and below the range due to equi- 
librium action. Hence it is we have the 21 feet 
rise and fall at Dover. The very little rise and 
fall at Portland is also illustrated in the upper- 
most figure of this diagram (Fig. 24). Thus high 
water at Dover is low water at Land's End, and 
the water seesaws as it were about a line going 
across from Portland to Havre (represented by 
N in the figure) ; not a line going directly across 
however, for on the other side of the Channel 
there is a curious complication. 

At the time of high water at Dover there is 
hardly any current in the Channel. As soon as 
the water begins to fall at Dover the current 
begins to flow west through the whole of the 
Channel. When it is mid-tide at Dover the tide 


is flowing fastest in the Channel. This was first 
brought to light by Admiral Beechey. 

I wish I had time to show the similar theory 
as to the tides in the Irish Channel. The water 
runs up the English Channel to Dover, and up 
the Irish Channel to fill up the basin round the 
Isle of Man. Take the northern mouth of the 
Irish Channel between the Mull of Cantire and 
the north-east coast of Ireland. The water rushes 
in through the straits between Cantire and Rathlin 
Island, to fill up the Bay of Liverpool and the 
great area of water round the Isle of Man. This 
tidal wave entering from the north, running south- 
ward through the Channel, meets in the Liverpool 
basin with the tidal stream coming from the 
south entrance, and causes the time of high 
water at Liverpool to be within half-an-hour of 
the time of no currents in the northern and 
southern parts of the Channel. 

I would like to read you the late Astronomer- 
Royal's appreciation of Laplace's splendid work 
on the tides. 

Airy says of Laplace : " If now, putting from 


our thoughts the details of the investigation, we 
consider its general plan and objects, we must 
allow it to be one of the most splendid works of 
the greatest mathematician of the past age. To 
appreciate this, the reader must consider, first, 
the boldness of the writer, who, having a clear 
understanding of the gross imperfections in the 
methods of his predecessors, had also the cour- 
age deliberately to take up the problem on 
grounds fundamentally correct (however it might 
be limited by suppositions afterwards introduced) ; 
secondly, the general difficulty of treating the 
motion of fluids ; thirdly, the peculiar difficulty 
of treating the motions when the fluids cover an 
area which is not plane but convex ; and fourthly, 
the sagacity of perceiving that it was necessary 
to consider the earth as a revolving body, and 
the skill of correctly introducing this considera- 
tion. This last point alone, in our opinion, gives 
a greater claim for reputation than the boasted 
explanation of the long inequality of Jupiter and 

Tidal theory must be carried on along with tidal 


FIG. 25. Tide Gauge. 

observations. Instruments for measuring and re- 
cording the height of the water at any time give 


us results of observations. 1 Here is such an 
instrument a tide gauge (Fig. 25). The floater 
is made of thin sheet copper, and is suspended by 
a fine platinum wire. The vertical motion of the 
floater, as the water rises and falls, is transmitted, 
in a reduced proportion by a single pinion and 
wheel, to this frame or marker, which carries a 
small marking pencil. The paper on which the 
pencil marks the recording curve, is stretched on 
this cylinder, which, by means of the clockwork, 
is caused to make one revolution every twenty- 
four hours. The leaning-tower-of-Pisa arrange- 
ment of the paper-cylinder, and the extreme 
simplicity of the connection between marker 
and floater, constitute the chief novelty. This 
tide-gauge is similar to one now in actual use, 
recording the rise and fall of the water in the 
River Clyde, at the entrance to the Queen's 
Dock, Glasgow. A sheet bearing the curves 

1 The various instruments and tide-curves referred to in this lecture 
are fully described and illustrated in a paper on " The Tide Gauge, 
Tidal Harmonic Analyser, and Tide Predicter " read before the In- 
stitution of Civil Engineers, on 1st March, 1881, and published in 
their Proceedings for that date. 



(Fig. 26) traced by that machine during a week 
is exhibited. 

After the observations have been taken, the next 
thing is to make use of them. Hitherto this has 
been done by laborious arithmetical calculation. I 
hold in my hand the Reports of the late Tidal 
Committee of the British Association with the 
results of the harmonic analysis about eight years' 
work carried on with great labour, and by aid of 
successive grants from the British Association. 
The Indian Government has continued the har- 
monic analysis for the seaports of India. The 
Tide Tables for Indian Ports for tJie Year 1882, 
issued under the authority of the Indian Govern- 
ment, show this analysis as in progress for the 
following ports, viz. : Aden, Kurrachee, Okha 
Point and Beyt Harbour at the entrance to 
the Gulf of Cutch, Bombay, Karwar, Beypore, 
Paumben Pass, Madras, Vizagapatam, Diamond 
Harbour, Fort Gloster and Kidderpore on the 
River Hooghly, Rangoon, Moulmein, and Port 
Blair. Mr. Roberts, who was first employed as 
calculator by the Committee of the British Asso- 


elation, has been asked to carry on the work 
for the Indian Government, and latterly, in 
India, native calculators under Major Baird, have 
worked by the methods and forms by which Mr. 
Roberts had worked in England for the British 
Association. 1 The object is to find the values of 
the different tidal constituents. We want to 
separate out from the whole rise and fall of the 
ocean the part due to the sun, the part due to 
the moon, the part due to one portion of the 
moon's effect, and the part due to another. There 
are complications depending on the moon's position 
declinational tides according as the moon is or 
is not in the plane of the earth's equator and 
also on that of the sun. Thus we have the diurnal 
declinational tides. When the moon is in the north 
declination (Fig. 27) we have (in the equilibrium 
theory) higher water at lunar noon than at lunar 
midnight. That difference in the height of high- 

1 Note of September 17, 1887. On the subject of Tidal Har- 
monic Analysis see " Manual of Instructions for Tidal Observa- 
tion," by Major Baird, published by Messrs. Taylor and Francis, 
London, 1886 ; also the Reports of the British Association Com- 
mittee "On Harmonic Analysis of Tidal Observations." W. T. 


water, and the corresponding solar noon tides and 
solar midnight tides, due to the sun not being 
in the earth's equator, constitute the lunar and 
solar diurnal declinational tides. In summer 
the noon high water might be expected to be 
higher than the midnight high water, because 

FIG. 27. Declinational Tide. 

the sun is nearer overhead to us than to our 

By kind permission of Sir Frederick Evans, I am 
able to place before you these diagrams of curves 
drawn by Captain Harris, R.N., of the Hydrographic 
Department of the Admiralty, exhibiting the rise 
and fall of tides in Princess Royal Harbour, King 
George Sound, Western Australia, from January 


ist to December 3ist, 1877, and in Broad Sound, 
Queensland, Australia, from July I5th, 1877, to 
July 23rd, 1878. Look at this one of these 
diagrams/a diagram of the tides at the north-east 
corner of Australia. For several days high water 
always at noon. When the tides are noticeable at 
all we have high water at noon, and when the tides 
are not at noon they are so small that they are not 
taken notice of at all. It thus appears as if the 
tides were irrespective of the moon, but they are 
not really so. When we look more closely, it is 
a full moon if we have a great tide at noon ; or 
else it is new moon. It is at half moon that we 
have the small tides, and when they are smallest 
we have high water at six. There is also a great 
difference between day and night high water ; the 
difference between them is called the diurnal tide. 
A similar phenomenon is shown on a smaller 
scale in this curve, drawn by the first tide-pre- 
dicting machine. At a certain time the two 
high waters become equalised, and the two low 
waters very unequal (see p. 172 for real examples). 
The object of the harmonic analysis is to analyse 


out from the complicated curve traced by the tide- 
gauge the simplest harmonic elements. A simple 
harmonic motion may be imagined as that of a 
body which moves simply up and down in a 
straight line, keeping level with the end of a clock 
hand, moving uniformly round. The exceedingly 
complicated motion that we have in the tides is 
analysed into a scries of simple harmonic motions 
in different periods and with different amplitudes 
or ranges ; and these simple harmonic constituents 
added together give the complicated tides. 

All the work hitherto done has been accom- 
plished by sheer calculation ; but calculation of 
so methodical a kind that a machine ought to 
be found to do it. The Tidal Harmonic Analyser 
consists of an application of Professor James 
Thomson's disk-globe-and-cylinder integrator to 
the evaluation of the integrals required for the 
harmonic analysis. The principle of the machine 
and the essential details are fully described and 
explained in papers communicated by Professor 
James Thomson and the author to the Royal 
Society, in 1876 and 1878, and published in the 
VOL. in. N 


Proceedings for those 
years ; l also reprinted, with 
a postscript dated April 
1879, in Thomson and 
Tait's Natural Philosophy, 
Second Edition, Appendix 
B. It remains now to 
describe and explain the 
actual machine referred to 
in the last of these com- 
munications, which is the 
only tidal harmonic an- 
alyser hitherto made. It 
may be mentioned, how- 
ever, in passing, that a 
similar instrument, with 
the simpler construction 
wanted for the simpler har- 
monic analysis of ordinary 
meteorological phenomena, 
has been constructed for the 

1 Vide vol. xxiv. p. 262, and vol. 
xxvii. p. 371. 


Meteorological Committee, and is now regularly 
at work at their office, harmonically analysing 
the results of meteorological observations, under 
the superintendence of Mr. R. H. Scott. 

Fig. 28 represents the tidal harmonic analyser, 
constructed under the author's direction, with the 
assistance of a grant from the Government Grant 
Fund of the Royal Society. The eleven cranks 
of this instrument are allotted as follows : 





i and 2 

To find the mean lunar semi-diurnal tide . . . 


2( y -a) 

3 4 

,, mean solar ,, ,, . . . 


2 (r-*) 

5 6 

,, luni-solar declinational diurnal tide 



7 8 

,, slower lunar ,, ,, 


9 10 

,, slower solar ,, ,, 
,, mean water level 


A ff 


The general arrangement of the several parts 
may be seen from Fig. 28. The large circle at 
the back, near the centre, is merely a counter to 
count the days, months, and years for four years, 
being the leap year period. It is driven by a 

N 2 


worm carried on an intermediate shaft, with a 
toothed wheel geared on another on the solar 
shaft. In front of the centre is the paper drum, 
which is on the solar shaft, and goes round in the 
period corresponding to twelve mean solar hours. 
On the extreme left, the first pair of disks, with 
globes and cylinders, and crank shafts with cranks 
at right angles between them, driving their two 
cross-heads, corresponds to the K v or luni-solar 
diurnal tide. The next pair of disk-globe-and- 
cylinders corresponds to M, or the mean lunar 
semi-diurnal tide, the chief of all the tides. The 
next pair lie on the two sides of the main shaft 
carrying the paper drum, and correspond to S, 
the mean solar semi-diurnal tide. The first pair 
on the right correspond to O, or the lunar diurnal 
tide. The second pair on the right correspond to 
P, the solar diurnal tide. The last disk on the 
extreme right is simply Professor James Thom- 
son's disk-globe-and-cylinder integrator, applied to 
measure the area of the curve as it passes through 
the machine. 

The idle shafts for the M and the O tides are 


seen in front respectively on the left and right of 
the centre. The two other longer idle shafts for 
the K and the P tides are behind, and therefore 
not seen. That for the P tide serves also for the 
simple integrator on the extreme right. 

The large hollow square brass bar, stretching 
from end to end along the top of the instrument, 
and carrying the eleven forks rigidly attached to 
it, projecting downwards, is moved to and fro 
through the requisite range by a rack and pinion, 
worked by a handle and crank in front above the 
paper cylinder, a little to the right of its centre. 
Each of these eleven forks moves one of the 
eleven globes of the eleven disk-globe-and-cylinder 
integrators of which the machine is composed. 
The other handle and crank in front, lower down 
and a little to the left of the centre, drives by a 
worm, at a conveniently slow speed, the solar 
shaft, and through it, and the four idle shafts, the 
four other tidal shafts. 

To work the machine the operator turns with 
his left hand the driving crank, and with his right 
hand the tracing crank, by which the fork-bar is 


moved. His left hand he turns always in one 
direction, and at as nearly constant a speed as is 
convenient to allow his right hand, alternately in 
contrary directions, to trace exactly with the steel 
pointer the tidal curve on the paper, which is 
carried across the line of to-and-fro motion of the 
pointer by the revolution of the paper drum, of 
which the speed is in simple proportion to the 
speed of the operator's left hand. 

The eleven little counters of the cylinders in 
front of the disks are to be set each at zero at the 
commencement of an operation, and to be read off 
from time to time during the operation, so as to 
give the value of the eleven integrals for as many 
particular values of the time as it is desired to have 

A first working model harmonic analyser, which 
served for model and for the meteorological analyser, 
now at work in the Meteorological Office, is here 
before you. It has five disk-globe-and-cylinders, 
and shafting geared for the ratio I : 2. Thus it 
serves to determine, from the deviation curve, the 
celebrated "ABCDE"of the Admiralty Com- 


pass Manual, this is to say, the coefficients in the 
harmonic expression 

A + B sin e + C cos 9 + D sin 2 6 + E cos 2 Q, 

for the deviation of the compass in an iron ship. 

The first instrument which I designed and 
constructed for use as a Tide Predicter was 
described in the Catalogue of the Loan Collec- 
tion of Scientific Apparatus at South Kensington 
in 1876; and the instrument itself was presented 
by the British Association to the South Kens- 
ington Museum, where it now is. The second in- 
strument constructed on the same principle is in 
London, and is being worked under the direction of 
Mr. Roberts, analysing the tides for the Indian ports. 
The result of this work is these books (Tide Tables 
for Indian Ports) in which we have, for the first 
time, tables of the times and heights of high water 
and low water for fourteen of the Indian ports. 

To predict the tides for the India and China 
Seas and Australia we have a much more difficult 
thing to do than for the British ports. The 
Admiralty Tide Tables give all that is necessary 
for the British ports, practically speaking ; but for 


other parts of the world generally the diurnal tide 
comes so much into play that we have exceedingly 
complicated action. The most complete thing 

FIG. 29. Tide Predictor. 

would be a table showing the height of the water 
every hour of the twenty-four. No one has yet 
ventured to do that generally for all parts of the 
world ; but for the comparatively complicated tides 


of the India Seas, the curves traced by the Tide- 
Predicter from which is obtained the information 
given in these Indian tide tables, do actually tell 
the height of the water for every instant of the 
twenty-four hours. 

The mechanical method which I have utilised 
in this machine is primarily due to the Rev. F. 
Bashforth who, in 1845, when he was a Bachelor 
of Arts and Fellow of St. John's College, 
Cambridge, described it to Section A of the 1845 
(Cambridge) meeting of the British Association 
in a communication entitled " A Description of a 
Machine for finding the Numerical Roots of 
Equations and tracing a Variety of Useful Curves," 
of which a short notice appears in the British 
Association Report for that year. The same 
subject was taken up by Mr. Russell in a com- 
munication to the Royal Society in 1869, "On 
the Mechanical Description of Curves," l which 
contains a drawing showing mechanism sub- 
stantially the same as that of the Tide Predictor. 
Here is the principle as embodied in No. 3 Tide 

1 Prof. Royal Society, June 17, 1869; (vol. xviii. p. 72). 


Predictor (represented in Fig. 29, p. 184), now 
actually before you: 

A long cord of which one end is held fixed 
passes over one pulley, under another, and so on. 
These eleven pulleys are all moved up and down 
by cranks, and each pulley takes in or lets out 
cord according to the direction in which it moves. 
These cranks are all moved by trains of wheels 
gearing into the eleven wheels fixed on this driving 
shaft. The greatest number of teeth on any wheel 
is 802 engaging with another of 423. All the 
other wheels have comparatively small numbers of 
teeth. The machine is finished now, except a 
cast-iron sole and cast-iron back. A fly-wheel of 
great inertia enables me to turn the machine fast, 
without jerking the pulleys, and so to run off a 
year's curve in about twenty-five minutes. This 
machine is arranged for fifteen constituents in all 
and besides that there is an arrangement for 
analysing out the long period tides. 

The following table shows how close an 
approximation to astronomical accuracy is given 
by the numbers chosen for the teeth of the several 



wheels. These numbers I have found by the 
ordinary arithmetical progress of converging 


Speed in Degrees per Mean Solar Hour. 

Losses of Angle in 


As given by Machine. 

Per Mean 
Solar Hour. 



28 9841042 

15 X = 28' 9 84o630 

-f- 0'00004I2 



, 5 ., 4 ,o6S6 

15 X 365 = 15 '0410959 

o '0000267 

o-n 7 

I 3 ' "94 30356 

15 X 369 = I3 '943 8 94 

- o 0000538 

o-23 7 




+ o '0000242 

o"'n 9 




+ o*ooooi33 



2 9 ? '5284783 15 X ~g = 2^-5283018 

+ o-^, 77 

o 78 


,8- 5 , 25 830 

sxgf = =8- 5 ,=3966 

+ o'ocoi864 

o 82 

M S 

5 8-. 9 8 4 ,o 42 

230 271 

15 X - X = 58 '9836600 

+ 0-000444 



27 '9682084 


15 X 251 - 2 7 '963i2 7S 

+ o'oooo8o 9 



2 9'4556254 

15 X 2^48 = 2 9'455645i 

- o '0000197 




15 X ^ = 13 3986928 

- o'oooo3i8 

o-i 4 

To-day (Aug. 25, 1882), a committee, consisting 
of only two members, Mr. George Darwin and 


Professor Adams of Cambridge, have been ap- 
pointed, and one of their chief objects will be to 
examine the long period tides [see note to p. 203]. 
There is one very interesting point I said I 
would endeavour to speak of if I had time ; I 
have not time, but still I must speak of it the 
influence of the moon on the weather. "We 
almost laugh when we hear of the influence of 
the moon on the weather," Sir F. Evans said 
to me, "but there is an influence." Gales of 
wind are remarkably prevalent in Torres Straits 
and the neighbourhood about the time of new 
and full moon. This was noticed by Dr. Rattray, 
a surgeon in the navy, in connection with obser- 
vations made by the surveying ship, Ffy, during 
the three years 1841-44. Dr. Rattray noticed 
that at those times there was a large area of coral 
reef uncovered at the very low water of the 
spring tides, extending out some sixty or seventy 
miles from land. This large area becomes highly 
heated, and the great heating of that large portion 
of land gives rise to a tendency to gales at the 
full and change, that is at the new and full moon. 


This indirect effect of the moon upon the weather 
through the tides is exceedingly interesting ; but 
it does not at all invalidate the scientific con- 
clusion that there is no direct influence, and the 
general effect of the moon on the weather the 
changes in the moon and the changes in the 
weather, and their supposed connection remains 
a mere chimsera. 

The subject of elastic tides in which the yielding 
of the solid earth is taken into account is to be 
one of the primary objects of Mr. G. Darwin's com- 
mittee. The tide-generating force which tends to 
pull the water to and from the moon, tends to 
pull the earth also. Imagine the earth made of 
india-rubber and pulled out to and from the moon. 
It will be made prolate (Fig. 30). If the earth were 
of india-rubber the tides would be nothing, the 
rise and fall of the water relatively to the solid 
would be practically nil. If the earth (as has 
long been a favourite hypothesis of geologists) 
had a thin shell 20 or 30 miles thick with liquid 
inside, there would be no such thing as tides of 
water rising and falling relatively to land, or sea- 


bottom. The earth's crust would yield to and 
from the moon, and the water would not move at 
all relatively to the crust. If the earth were even 
as rigid as glass all through, calculation shows that 
the solid would yield so much that the tides could 
only be about one third of what they would be if 
the earth were perfectly rigid. Again, if the earth 
were two or three times as rigid as glass, about as 
rigid as a solid globe of steel, it would still, con- 

FIG. 30. Elastic Tides. 

sidering its great dimensions, yield two or three feet 
to that great force, which elastic yielding would 
be enough to make the tides only twc thirds of 
what they would be if the earth were perfectly 
rigid. Mr. G. Darwin has made the investigation 
by means of the lunar fortnightly tides, and the 
general conclusion, subject to verification, is that the 
earth does seem to yield somewhat, and may have 
something like the rigidity of a solid globe of steel. 

THE TIDES, (APP. A.] 191 


[Extracts from a Lecture on " The Tides" given to the 
Glasgow Science Lectures Association, not hitherto pub- 
lished, and now included as explaining in greater detail 
certain paragraphs of the preceding Lecture.] 

(i) Gravitation. The great theory of gravitation 
put before us by Newton asserts that every portion 
of matter in the universe attracts every other por- 
tion ; and that the force depends on the masses of 
the two portions considered, and on the distance be- 
tween them. Now, the first great point of Newton's 
theory is, that bodies which have equal masses are 
equally attracted by any other body, a body of 
double mass experiencing double force. This may 
seem only what is to be expected. It would take 
more time than we have to spare were I to point 
out all that is included in this statement ; but let 
me first explain to you how the motions of dif- 
ferent kinds of matter depend on a property called 
inertia. I might show you a mass of iron as here. 
Consider that if I apply force to it, it gets into a 
state of motion ; greater force applied to it, during 


the same time, gives it increased velocity, and so 
on. Now, instead of a mass of iron, I might hang 
up a mass of lead, or a mass of wood, to test the 
equality of the mass by the equality of the motion 
which is produced in the same time by the action 
of the same force, or in equal times by the action 
of equal forces. Thus, quite irrespectively of the 
kind of matter concerned, we have a test of the 
quantity of matter. You might weigh a pound of 
tea against a pound of brass without ever putting 
them into the balance at all. You might hang up 
one body by a proper suspension, and you might, 
by a spring, measure the force applied, first to the 
one body, and then to the other. If the one body 
is found to acquire equal velocity under the in- 
fluence of equal force for equal times as compared 
with the other body, then the mass of the one is 
said to be equal to the mass of the other. 

I have spoken of mutual forces between any 
two masses. Let us consider the weight or heavi- 
ness of a body on the earth's surface. Newton 
explained that the attraction of the whole earth 
upon a body for example, this 56 pounds mass 
of iron causes its heaviness or weight. Well, 
now, take 56 pounds of iron here, and take a 
mass of lead, which, when put in the balance, 
is found to be of equal weight. You see we 
have quite a new idea here. You weigh this 
mass of iron against a mass of lead, or to 
weigh out a commodity for sale ; as, for instance, 

THE TIDES. (APP. A.} 193 

to weigh out pounds of tea, to weigh them with 
brass weights is to compare their gravitations 
towards the earth to compare the heavinesses of 
the different bodies. But the first subject that 
I asked you to think of had nothing to do with 
heaviness. The first subject was the mass of the 
different bodies as tested by their resistance to 
force tending to set them in motion. I may just 
say that the property of resistance against being 
set into motion, and again against resistance to 
being stopped when in motion, is the property of 
matter called inertia. 

The first great point in Newton's discovery 
shows, then, that if the property of inertia is 
possessed to an equal degree by two different 
substances, they have equal heaviness. One of 
his proofs was founded on the celebrated guinea 
and feather experiment, showing that the guinea 
and feather fall at the same rate when the resist- 
ance of the air is removed. Another was founded 
upon making pendulums of different substances 
lead, iron, and wood to vibrate, and observing 
their times of vibration. Newton thus dis- 
covered that bodies which have equal heaviness 
have equal inertia. 

The other point of the law of gravitation is, that 
the force between any two bodies diminishes as 
the distance increases, according to the law of the 
inverse square of the distance. That law expresses 
that, with double distance, the force is reduced one 

VOL. in. O 


quarter, at treble distance the force is reduced to 
one-ninth part. Suppose we compare forces at the 
distance of one million miles, then again at the 
distance of two and a half million miles, we have 
to square the one number then square the other, 
and find the proportion of the square of the one 
number to the square of the other. The forces are 
inversely as the squares of the distance, that is the 
most commonly quoted part of the law of gravita- 
tion ; but the law is incomplete without the first 
part, which establishes the relation between two 
apparently different properties of matter. Newton 
founded this law upon a great variety of different 
natural phenomena. The motion of the planets 
round the sun, and the moon round the earth, 
proved that for each planet the force varies 
inversely as the square of its distance from the 
sun ; and that from planet to planet the forces on 
equal portions of their masses are inversely as the 
squares of their distances. The last link in the 
great chain of this theory is the tides. 

(2) Tide-Generating Force. And now we are 
nearly ready to complete the theory of tide- 
generating force. The first rough view of the case, 
which is not always incorrect, is that the moon 
attracts the waters of the earth towards herself and 
heaps them up, therefore, on one side of the earth. 
It is not so. It would be so if the earth and moon 
were at rest and prevented from falling together 
by a rigid bar or column. If the earth and 

THE TIDES. (APP. A.} 195 

moon were stuck on the two ends of a strong 
bar, and put at rest in space, then the attrac- 
tion of the moon would draw the waters of the 
earth to the side of the earth next to the moon. 
But in reality things are very different from that 
supposition. There is no rigid bar connecting the 
moon and the earth. Why then does not the moon 
fall towards the earth ? According to Newton's 
theory, the moon is always falling towards the earth. 
Newton compared the fall of the moon, in his 
celebrated statement, with the fall of a stone at the 
earth's surface, as he recounted, after the fall of an 
apple from the tree, which he perceived when sit- 
ting in his garden musing on his great theory. 
The moon is falling towards the earth, and falls in 
an hour as far as a stone falls in a second. It 
chances that the number 60 is nearly enough, as I 
have said before, a numerical expression for the dis- 
tance of the moon from the earth in terms of the 
earth's radius. It is only by that chance that the 
comparison between the second and hour can be here 
introduced. Since there are 60 times 60 seconds 
in an hour, and about 60 radii of the earth in 
the distance from the moon, we are led to the 
comparison now indicated, but I am inverting the 
direction of Newton's comparison. He found by 
observation that the moon falls as far in an hour as 
a stone falls in a second, and hence inferred that 
the force on the moon is a 6oth of the 6oth of the 
force per equal mass on the earth's surface. Then 

O 2 



he learned from accurate observations, and from the 
earth's dimensions, what I have mentioned as the 
moon's distance, and perceived the law of variation 
between the weight of a body at the earth's surface 
and the force that keeps the moon in her orbit. 
The moon in Newton's theory was always falling 
towards the earth. Why does it not come down ? 
Can it be always falling and never come down ? 
That seems impossible. It is always falling, but it 
has also a motion perpendicular to the direction in 
which it is falling, and the result of that continual 
falling is simply a change of direction of this 

It would occupy too much of our time to go into 
this theory. It is simply the dynamical theory of 
centrifugal force. There is a continual falling 
away from the line of motion, as illustrated in a 
stone thrown from the hand describing an ordinary 
curve. You know that if a stone is thrown hori- 
zontally it describes a parabola the stone falling 
away from the line in which it was thrown. The 
moon is continually falling away from the line in 
which it moves at any instant, falling away towards 
the point of the earth's centre, and falling away 
towards that point in the varying direction from 
itself. You can see it may be always falling, no\v 
from the present direction, now from the altered 
direction, now from the farther altered direction in 
a further altered line ; and so it may be always 
falling and never coming down. The parts of the 

THE TIDES. (APP. A.} 197 

moon nearest to the earth tend to fall most rapidly, 
the parts furthest from the earth, least rapidly ; in 
its own circle, each is falling away and the result is 
as if we had the moon falling directly. 

But while the moon is always falling towards the 
earth, the earth is always falling towards the moon ; 
and each preserves a constant distance, or very 
nearly a constant distance from the common centre 
of gravity of the two. The parts of the earth 
nearest to the moon are drawn towards the 
moon with more force than an equal mass at 
the average distance ; the most distant parts are 
drawn towards the moon with less force than 
corresponds to the average distance. The solid 
mass of the earth, as a whole, experiences y 
according to its mass, a force depending on the 
average distance ; while each portion of the water 
on the surface of the earth experiences an attractive 
force due to its own distance from the moon. The 
result clearly is, then, a tendency to protuberance 
towards the moon and from the moon ; and thus, 
in a necessarily most imperfect manner, I have 
explained to you how it is that the waters are not 
heaped up on the side next the moon, but are 
drawn up towards the moon and left away from 
the moon so as to tend to form an oval figure. 
The diagram (Fig. 21, p. 161) shows the pro- 
tuberance of water towards and from the moon. 
It shows also the sun on the far side, I need 
scarcely say, with an enormous distortion of 


proportions, because without that it would be 
impossible in a diagram to show the three 
bodies. This illustrates the tendency of the 
tide-generating forces. 

(3) Elastic Tides. But another question arises. 
This great force of gravity operating in different 
directions, pulling at one place, pressing in at 
another, will it not squeeze the earth out of 
shape ? I perceive signs of incredulity ; you think 
it impossible it can produce any sensible effect. 
Well, I will just tell you that instead of being im- 
possible, instead of it not producing any such 
effect, we have to suppose the earth to be of 
exceedingly rigid material, in order that the effect 
of these distorting influences on it may not mask 
the phenomenon of the tides altogether. 

There is a very favourite geological hypothesis 
which I have no doubt many here present have 
heard, which perhaps till this moment many here 
present have believed, but which I hope no one 
w r ill go out of this room believing, and that is that 
the earth is a mere crust, a solid shell thirty, or 
forty, or fifty miles thick at the most, and that it is 
filled with molten liquid lava. This is not a sup- 
position to be dismissed as absurd, as ludicrous, as 
absolutely unfounded and unreasonable. It is a 
theory based on hypothesis which requires most 
careful weighing. But it has been carefully weighed 
and found wanting in conformity to the truth. On 
a great many different essential points it has been 

THE TIDES. (A PP. A.) 199 

found at variance with the truth. One of these 
points is, that unless the material of this supposed 
shell were preternaturally rigid, were scores of 
times more rigid than steel, the shell would yield so 
freely to the tide-generating forces that it would 
take the figure of equilibrium, and there would be 
no rise and fall of the water, relatively to the solid 
land, left to show us the phenomena of the tides. 

Imagine that this (Fig. 30, p. 190) represents a 
solid shell with water outside, you can understand if 
the solid shell yields with sufficiently great freedom, 
there will be exceedingly little tidal yielding left 
for the water to show. It may seem strange when 
I say that hard steel would yield so freely. But 
consider the great hardness of steel and the smaller 
hardness of india-rubber. Consider the greatness 
of the earth, and think of a little hollow india- 
rubber ball, how freely it yields to the pressure of 
the hand, or even to its own weight when laid on a 
table. Now, take a great body like the earth : the 
greater the mass the more it is disposed to yield to 
the attraction of distorting forces when these forces 
increase with the whole mass. I cannot just 
now fully demonstrate to you this conclusion ; 
but I say that a careful calculation of the 
forces shows that in virtue of the greatness of 
the mass it would require an enormously in- 
creased rigidity in order to keep in shape. So 
that if we take the actual dimensions of the 
earth at forty-two million feet diameter, and the 


crust at fifty miles thick, or two hundred and 
fifty thousand feet, and with these proportions 
make the calculation, we find that something scores 
of times more rigid than steel would be required to 
keep the shape so well as to leave any appreci- 
able degree of difference from the shape of hydro- 
static equilibrium, and allow the water to indicate, 
by relative displacement, its tendency to take the 
figure of equilibrium ; that is to say, to give us 
the phenomena of tides. The geological inference 
from this conclusion is, that not only must we 
deny the fluidity of the earth and the assertion 
that it is encased by a thin shell, but we must 
say that the earth has, on the whole, a rigidity 
greater than that of a solid globe of glass of the 
same dimensions ; and perhaps greater than that 
of a globe of steel of the same dimensions. But 
that it cannot be less rigid than a globe of glass, 
we are assured. It is not to be denied that there 
may be a very large space occupied by liquid. We 
know there are large spaces occupied by lava ; but 
we do not know how large they may be, although 
we can certainly say that there are no such spaces, 
as can in volume be compared with the supposed 
hollow shell, occupied by liquid constituting the 
interior of the earth. The earth as a whole 
must be rigid, and perhaps exceedingly rigid, 
probably rendered more rigid than it is at the 
surface strata by the greater pressure in the 
greater depths. 

THE TIDES. (APP. B.) 201 

The phenomena of underground temperature, 
which led geologists to that supposition, are 
explained otherwise than by their assumption of a 
thin shell full of liquid ; and further, every view 
we can take of underground temperature, in the 
past history of the earth, confirms the statement 
that we have no right to assume interior fluidity. 



[Abstract of a paper read at the Dublin (1878) meeting 
of the British Association.'} 

THE conclusions are : 

I. The rise and fall of the water-surface and 
the tidal streams throughout the North Sea, north 
of the parallel of 53 (through Cromer, in Norfolk), 
and on the north coasts of Holland and Hanover, 
are not sensibly different from what they would be 
if the passage through the Straits of Dover were 
stopped by a barrier. 

2. The main features of the tides (rise and fall 


and tidal streams) throughout the British Channel 
west of Beachy Head and St. Valery-en-Caux, do 
not differ much from what they would be if the pas- 
sage through the Straits were stopped by a barrier 
between Dover and Cape Grisnez (Calais). 

3. A partial effect of the actual current through 
the Straits is to make the tides throughout the 
Channel, west of a line through Hastings to the 
mouth of the Somme, more nearly agree with what 
they would be were there a barrier along this line, 
than what they would be if there were a barrier 
between Dover and Cape Grisnez. 

4. The chief obviously noticeable effect of the 
openness of the Straits of Dover on tides west of 
Beachy Head is that the rise and fall on the 
coast between Christchurch and Portland is not 
much smaller than it is. 

5. The fact that the tidal currents commence 
flowing westward generally an hour or two before 
Dover high-water, and eastward an hour or two 
before Dover low-water, instead of exactly at the 
times of Dover high and low-water, is also partially 
due to the openness of the Straits of Dover. 

6. The facts referred to in Nos. 4 and 5 are 
no doubt partially due also to fluid friction (in 
eddies along the bottom and in tide-races), and 
want of absolute simultaneity in the time of high- 
water across the mouth of the Channel from Land's 
End to Ushant. Without farther investigation it 
would be in vain to attempt to estimate the 

THE TIDES. (APP. B) 203 

proportionate contributions of the three causes to 
the whole effect. 

7. According to Fourier's elementary principles 
of harmonic analysis all deviations from regular 
simple harmonic rise and fall of the tide within 
twelve hours are to be represented by the super- 
position of simple harmonic oscillations in six- 
hours period, and four-hours period, and three-hours 
period, and so on like the " overtones " which give 
the peculiar characters to different musical sounds 
of the same pitch. The six-hourly oscillation 
which gives the double low-water at Portland and 
the protracted duration of the high-water at Havre * 
is probably in part due to the complex-harmonic 
character of the current through the Straits of 
Dover ; that is to say, definitely, to a six-hourly 
periodic term in the Fourier-series representing the 
quantity of water passing through the Straits 
per unit of time, at any instant of the twelve 

8. The double high-water experienced at South- 
ampton, and in the Solent, and at Christchurch 
and Poole, and still further west, generally attributed 
to the doubleness of the influence experienced 
from the tidal streams on the two sides of the Isle 

1 At Havre, on the French coast, the high- water remains station- 
ary for one hour, with a rise and fall of three or four inches for 
another hour, and only rises and falls thirteen inches for the space of 
three hours ; this long period of nearly slack water is very valuable to 
the traffic of the port, and allows from fifteen to sixteen vessels to 
enter or leave the docks on the same tide. 


of Wight, seems to have a continuity of cause with 
the double low-water at Portland, which is certainly 
allied to the protracted high-water of Havre a 
phenomenon quite beyond reach of the Solent's 
influence. It is probable, therefore, that the 
double high-water in the Solent and at Christ- 
church and Poole is influenced sensibly by the 
current through the Straits of Dover, even though 
the common explanation attributing them to the 
Isle of Wight may be in the main correct. 



[Abstract of paper by Captain Evans, R.N., F.R.S., and Sir 
William Thomson, LL.D., F.R.S., read in Section E of 
the Dubli?i (1878) meeting of t]ie British Association^ 

ON the coasts of the British Islands and 
generally on the European coasts of the North 
Atlantic and throughout the North Sea, the tides 
present in their main features an exceptional 
simplicity, two almost equally high high- waters and 
two almost equally low low-waters in the twenty- 
four hours, with the regular fortnightly inequality of 

THE TIDES. (APP. C) 205 

spring tides and neap tides due to the alternately 
conspiring and opposing actions of the moon and 
sun, and with large irregular variations produced 
by wind. Careful observation detects a small 
" diurnal " inequality (so called because it is due 
to tidal constituents having periods approximately 
equal to twenty-four hours lunar or solar), of which 
the most obvious manifestation is a difference at 
certain times of the month and of the year 
between the heights of the two high-waters of the 
twenty-four hours, and at intermediate times a 
difference between the heights of the two low- 

In the western part of the North Atlantic and in 
the North Sea, this diurnal inequality is so small in 
comparison with the familiar twelve-hourly or 
"semi-diurnal" tide that it is practically disre- 
garded, and its very existence is scarcely a part of 
practical knowledge of the subject ; but it is not so 
in other seas. There is probably no other great 
area of sea throughout which the diurnal tides are 
practically imperceptible and the semi-diurnal tides 
alone practically perceptible. In some places in 
the Pacific and in the China Sea it has long been 
remarked that there is but one high water in the 
twenty-four hours at certain times of the month, 
and in the Pacific, the China Sea, the Indian Ocean, 
the West Indies, and very generally wherever tides 
are known at all practically, except on the ocean 
coasts of Europe, they are known to be not 


" regular " according to the simple European rule, 
but to be complicated by large differences between 
the heights of consecutive high-waters and of con- 
secutive low-waters, and by marked inequalities of 
the successive intervals of time between high-water 
and low-water. 

On the coasts of the Mediterranean generally the 
tides are so small as to be not perceptible to 
ordinary observation, and nothing therefore has 
been hitherto generally known regarding their 
character. But a first case of application of the 
harmonic analysis to the accurate continuous 
register of a self-recording tide-gauge (published 
in the 1876 Report of the B.A. Tidal Committee) 
has shown for Toulon a diurnal tide amounting on 
an average of ordinary midsummer and mid-winter 
full and new moons to nearly 4/5 of the semi- 
diurnal tides ; and the present communication con- 
tains the results of analysis showing a similar result 
for Marseilles ; but on the other hand for Malta, a 
diurnal tide (similarly reckoned), amounting to 
only 2/9 of the semi-diurnal tide. The semi- 
diurnal tide is nearly the same amount in the three 
places, being at full and new moon, about seven 
inches rise and fall. 

The present investigation commenced in the 
Tidal Department of the Hydrographic Office, 
under the charge of Staff-Commander Harris, R.N., 
with an examination and careful practical analysis 
of a case greatly complicated by the diurnal in- 

THE TIDES. (APP. C) 207 

equality presented by tidal observations which had 
been made at Freemantle, Western Australia, in 
1873-74, chiefly by Staff-Commander Archdeacon, 
R.N., the officer in charge of the Admiralty Survey 
of that Colony. The results disclosed very re- 
markable complications, the diurnal tides pre- 
dominating over the semi-diurnal tides at some 
seasons of month and year, and at others almost 
disappearing and leaving only a small semi-diurnal 
tide of less than a foot rise and fall. These 
observations were also very interesting in respect to 
the great differences of mean level which they 
showed for different times of year, so great that 
the low-waters in March and April were generally 
higher than the high-waters in September and 
October. The observations were afterwards, under 
the direction of Captain Evans and Sir William 
Thomson, submitted to a complete harmonic 
analysis worked out by Mr. E. Roberts. Not only 
on account of the interesting features presented by 
this first case of analysis of tides of the southern 
hemisphere, but because the south circumpolar 
ocean has been looked to on theoretical grounds as 
the origin of the tides, or of a large part of the 
tides, of the rest of the world, it seemed desirable 
to extend the investigation to other places of the 
southern hemisphere for which there are available 
data. Accordingly the records in the Hydrographic 
Office of tidal observations from all parts of the 
world were searched, but besides those of Free- 


mantle, nothing from the southern hemisphere was 
found sufficiently complete for the harmonic 
analysis except a year's observations of a self-re- 
gistering tide-gauge at Port Louis, Mauritius, and 
personal observations made at regular hourly, and 
sometimes half-hourly, intervals for about six 
months (May to December) of 1842, at Port Louis, 
Berkeley Sound, East Falkland, under the direction 
of Sir James Clark Ross. These have been sub- 
jected to complete analysis. 

So also have twelve months' observations by a 
self-registering tide-gauge during 1871-2 at Malta, 
contributed by Admiral Sir A. Cooper Key, K.C.B., 

Tide-curves for two more years of Toulon (1847 
and 1848) in addition to the one (1853) previously 
analysed, and for Marseilles for a twelvemonth 
of 1850-51, supplied by the French Hydrographic 
Office, have also been subjected to the harmonic 

[The numerical results obtained will be found in 
Nature, October 24, 1878 (vol. xviii. p. 670).] 

THE TIDES. (APP. D.} 209 



{Circular issued by Sir William Thomson in December, 1867, 
to the members of the Committee, appoi?ited, on his sug- 
gestion, by the British Association in 1867 u For the 
Purpose of Promoting the Extension, Improvement, and 
Harmonic Analysis, of Tidal Observations."} 

[Brit is k Association Report, Norwich, 1868, p. 490.] 

i. The chief, it may be almost said the only, 
practical conclusion deducible from, or at least 
hitherto deduced from, the dynamical theory is, 
that the height of the water at any place may be 
expressed as the sum of a certain number of simple 
harmonic functions 1 of the time, of which the 
periods are known, being the periods of certain 
components of the sun's and moon's motions. 2 
Any such harmonic term will be called a tidal con- 
stituent, or sometimes, for brevity, a tide. The 
expression for it in ordinary analytical notation is 
A cos nt + B sin nt ; or R cos (nt e), if A = R 

1 See Thomson's and Tail's Natural Philosophy > 53, 54. 

2 See Laplace, Mecanique Celeste, liv. iv. 16. Airy's Tides and 
Waves, 585. 



cos e, and B = R sin e ; where t denotes time 
measured in any unit from any era, n the corre- 
sponding angular velocity (a quantity such that - 

is the period of the function), R and e the ampli- 
tude and the epoch, and A and B coefficients 
immediately determined from observation by the 
proper harmonic analysis (which consists virtually 
in the method of least squares applied to deduce 
the most probable values of these coefficients from 
the observations). 

2. The chief tidal constituents in most localities, 
indeed in all localities where the tides are compara- 
tively well known, are those whose periods are 
twelve mean lunar hours, and twelve mean solar 
hours respectively. Those which probably stand 
next in importance are the tides whose periods 
are approximately twenty-four hours. The former 
are called the lunar semidiurnal tide, and solar 
semidiurnal tide : the latter, the lunar diurnal tide 
and the solar diurnal tide. 1 There are, besides, the 
lunar fortnightly tide and the solar semiannual 
tide. 2 The diurnal and the semidiurnal tides have 
inequalities depending on the excentricity of the 
moon's orbit round the earth, and of the earth's 
round the sun, and the semidiurnal have inequali- 

1 See Airy's Tides and Waves, 46, 49 ; or Thomson and Tail's 
Natural Philosophy, 808. 

2 See Airy's Tides and Waves, 45 ; or Thomson and Tail's 
Natural Philosophy, 880. 

THE TIDES. (A PP. D.} 211 

ties depending on the varying declinations of the 
two bodies. Each such inequality of any one of 
the chief tides may be regarded as a smaller super- 
imposed tide of period approximately equal ; pro- 
ducing, with the chief tide, a compound effect 
which corresponds precisely to the discord of two 
simple harmonic notes in music approximately in 
unison with one another. These constituents may 
be called for brevity elliptic and declinational tides. 
But two of the solar elliptic diurnal tides thus 
indicated have the same period, being twenty-four 
mean solar hours. Thus we have in all twenty- 
three tidal constituents : 

Coefficients of / in arguments. 
Lunar. Solar. 

The lunar monthly ana solar \ 
annual (elliptic) . . . . / : 

The lunar fortnightly and ") 

solar semiannual (decli- > 2 20- 2/7 

national) ....... J 

The lunar and solar diurnal \ 
(declinational) J 

The lunar and solar semi- 

The lunar and solar elliptic "I 
diurnal J 

The lunar and solar elliptic 1 / 27 o--5> (27 T? 

semidiurnal J '" (27 3o--}-> (27 3/1 

The lunar and solar decli- ) 

national semidiurnal . . j 2 2y 2 ^ 

3. Here 7 denotes the angular velocity of the 
earth's rotation, and a, rj, & those of the moon's 

P 2 


revolution round the earth, of the earth's round the 
sun, and of the progression of the moon's perigee. 
The motion of the first point of Aries, and of the 
earth's perihelion, are neglected. It is almost 
certain that the slow variation of the lunar 
declinational tides due to the retrogression of the 
nodes of the moon's orbit, may be dealt with with 
sufficient accuracy according to the equilibrium 
method ; and the inequalities produced by the 
perturbations of the moon's motion are probably 
insensible. But each one of the twenty-three tides 
enumerated above is certainly sensible on our 
coasts. And there are besides, as Laplace has 
shown, very sensible tides depending on the fourth 
power of the moon's parallax, 1 the investigation of 
which must be included in the complete analysis 
now suggested, although for simplicity they have 
been left out of the preceding schedule. The 
amplitude and the epoch of each tidal constituent 
for any part of the sea is to be determined by 
observation, and cannot be determined except by 
observation. But it is to be remarked that the 
period of one of the lunar diurnal tides agrees with 
that of one of the solar diurnal tides, being 
twenty-four sidereal hours ; and that the period of 
one of the semidiurnal lunar declinational tides 
agrees with that of one of the semidiurnal solar de- 
clinational tides, being twelve sidereal hours. Also 

1 The chief effect of this at any one station is a ter-diurnal lunar 
tide, or one whose period is eight lunar hours. 

THE TIDES. (APP. /?.) 213 

that the angular velocities 7 <r -f- 5 and 7 cr & 
are so nearly equal, that observations through 
several years must be combined to distinguish the 
two corresponding elliptic diurnal tides. Thus 
the whole number of constituents to be determined 
by one year's observation is twenty. The forty 
constants specifying these twenty constituents are 
probably each determinable, with considerable 
accuracy, from the data afforded in the course of a 
year by a good self-registering tide-gauge, or from 
accurate personal observations taken at equal short 
intervals of time, hourly for instance. Each lunar 
declinational tide varies from a minimum to a 
maximum, and back to a minimum, every nineteen 
years or thereabouts (the period of revolution of the 
line of nodes of the moon's orbit). Observations 
continued for nineteen years will give the amount 
of this variation with considerable accuracy, and 
from it the proportion of the effect due to the 
moon will be distinguished from that due to the sun. 
It is possible that thus a somewhat accurate 
evaluation of the moon's mass may be arrived at. 

4. The methods of reduction hitherto adopted, 1 
after the example set by Laplace and Lubbock, 
have consisted chiefly, or altogether, in averaging 

1 See Directions for Reducing Tidal Observations ; by Staff- Com- 
mander Burdwood, London, 1865, published by the Admiralty ; 
also Professor Haughton on the " Solar and Lunar Diurnal Tides 
on the Coast of Ireland," Transactions of the Royal Irish Academy 
f^r April, 1854. 


the heights and times of high water and low water 
in certain selected sets of groups. Laplace com- 
menced in this way, as the only one for which 
observations made before his time were available. 
How strong the tendency is to pay attention chiefly 
or exclusively to the times and heights of high and 
low water, is indicated by the title printed at the top 
of the sheets used by the Admiralty to receive the 
automatic records of the tide-gauges ; for instance, 
" Diagram, showing time of high and low water at 
Ramsgate, traced by the tide-gauge." One of the 
chief practical objects of tidal investigation is, of 
course, to predict the time and height of high 
water ; but this object is much more easily and 
accurately attained by the harmonic reduction of 
observations not confined to high or low water. 
The best arrangement of observations is to make 
them at equi-distant intervals of time, and to 
observe simply the height of the water at the 
moment of observation irrespectively of the time 
of high or low water. This kind of observation 
will even be less laborious and less wasteful of time 
in practice than the system of waiting for high or 
low water, and estimating by a troublesome inter- 
polation the time of high water, from observations 
made from ten minutes to ten minutes, for some time 
preceding it and following it. The most complete 
system of observation is, of course, that of the 
self-registering tide-gauge which gives the height 
of the water-level above a fixed mark every instant. 

THE TIDES. (A PP. D.} 215 

But direct observation and measurement would 
probably be more accurate than the records of the 
most perfect tide-gauge likely to be realized. 

5. One object proposed for the Committee is to 
estimate the accuracy, both as to time and as to 
scale of height, attained by the best self-registering 
tide-gauges at present in use, and (taking into 
account also the relative costliness of different 
methods) to come to a resolution as to what method 
should be recommended when new sets of observa- 
tion are set on foot in any place. In the mean time 
the following method of observation is recommended 
as being more accurate and probably less expensive 
than the plan of measurement on a stem attached 
to a float, often hitherto followed where there is no 
self-registering tide-gauge. A metal tube, which 
need not be more than two or three inches in 
diameter, is to be fixed vertically, in hydrostatic com- 
munication by its lower end, with the sea. A metal 
scale graduated to centimetres (or to hundredths of a 
foot, if preferred) is to be let down by the observer 
in the middle of the tube until it touches the liquid 
surface ; and a fixed mark attached to the top of the 
tube then indicates the reading which is to be taken. 
Attached to the measuring-scale must be one or 
more pistons fitting loosely in the tube and guiding 
the rod so that it may remain, as nearly as may be, 
in the centre of the tube. The observer will know 
when its lower end is precisely at the level of the 
surface of the liquid, by aid of an electric circuit 


completed through a single galvanic cell, the coil 
of a common telegraph " detector," the metal 
measuring-scale, the liquid, and the metal tube. 1 
By this method it will be easy to test the position 
of the water-level truly to the tenth of an inch. 
It is not probable that tidal observations hitherto 
made, whether with self-registering tide-gauges or 
by direct observations, have had this degree of 
accuracy ; and it is quite certain that a proper 
method of reduction will take advantage of all 
the accuracy of the plan now proposed. 2 

6. An observation made on this plan every three 
hours, from day to day for a month, would pro- 
bably suffice to give the data required for nautical 
purposes for any harbour. It is intended immedi- 
ately to construct an apparatus of the kind, and 
give it a trial for a few weeks at some convenient 
harbour, and if the plan prove to be successful and 
convenient, it will come to be considered whether 
observations made at every hour of the day and 
night might not, all things considered (accuracy, 
economy, and sufficiency for all scientific wants) 
be preferable to a self-registering tide-gauge. 

1 Instead of the galvanic detector, a hydraulic method may be 
found preferable in some places. The latter consists in using a stiff 
tube of half inch diameter or so, instead of the solid metal 
measuring-bar, and testing whether its lower end is above or below 
the level of the water by suction at the upper end. 

2 The "Clyde Trust" have given permission to try this method 
at a convenient place in the harbour of Glasgow. It is probable 
that it will also be tried in the harbour of Belfast. 

THE TIDES. (A PP. A) 217 

/. One of the most interesting of the questions 
that can be proposed in reference to the tides is, 
how much is the earth's angular velocity diminished 
by them from century to century ? although the 
direct determination of this amount, or even a 
rough estimate of it, can scarcely be hoped for 
from tidal observation, as the data for the quad- 
rature required could not be had directly. But 
accurate observation of amounts and times of the 
tide on the shores of continents and islands of all 
seas might, with the assistance of improved 
dynamical theory, be fully expected to supply the 
requisite data for at least a rough estimate. In 
the mean time it may be remarked that one very 
important point of the theory, discovered by Airy, 1 
affords a ready means of disentangling some of 
the complication presented by the distribution of 
the times of high water in different places, and 
will form a sure foundation for the practical estimate 
of a definite part of the whole amount of retarda- 
tion, when the times of spring tides and neap tides 
are better known for all parts of the sea than they 
are at present. To understand this, imagine a tidal 
spheroid to be constructed by drawing an infinite 
number of lines perpendicular to the actual mean 
sea-level continued under the solid parts of the 
earth which lie above the sea, and equal to the 
spherical harmonic term or Laplace's function, of 

1 See Airy's Tides and Waves, 459. 


the second order, in the development of a discon- 
tinuous function equal to the height of the sea at 
any point above the mean level where there is sea, 
and equal to zero for all parts of the earth's surface 
occupied by dry land. This spheroid we shall call 
for brevity the mean tidal spheroid (lunar or solar 
as the case may be, or luni-solar when the heights 
due to moon and sun are added). The fact that the 
lunar semidiurnal tide is, over nearly the whole sur- 
face of the sea, greater than the solar, in a greater 
ratio than that of the generating force, renders it 
almost certain that the longest axes of the mean 
luni-tidal and soli-tidal spheroids would each of 
them lie in the meridian 90 from the disturbing 
body (moon or sun) if the motion of the water were 
unopposed by friction ; or, which means the same 
thing, that there would be on the average of the 
whole seas, low water when the disturbing body 
crosses the meridian, were the hypothesis of no fric- 
tion fulfilled. But, as Airy has shown, the tendency 
of friction is to advance the times of low and high 
water when the depth and shape of the ocean are 
such as to make the time of low water on the 
hypothesis of no friction be that of the disturbing 
body's transit. Now, the well-known fact that the 
spring tides on the Atlantic coast of Europe are 
about a day or a day and a half after full and 
change (the times of greatest force), and that 
through nearly the whole sea they are probably 
more or less behind these times, which Airy long 

THE TIDES. (APP. Z>.) 219 

ago maintained x to be a consequence of friction 
would prove that the crowns of the luni-tidal 
spheroid are in advance of those of the soli-tidal 
spheroid ; and therefore that those of the latter 
are less advanced by friction than those of the 
former. It is easily conceived that a know- 
ledge of the heights of the tides and of the 
intervals between the spring tides and the 
times of greatest force, somewhat more extensive 
than we have at present, would afford data for a 
rough estimate of the proper mean amount of the 
average interval in question, that is, of the interval 
between the times of high water of the mean luni- 
tidal and mean soli-tidal spheroids. The whole 
moment of the couple retarding the earth's rota- 
tion, in virtue of the lunar tide, must be something 
more than that calculated on the hypothesis that 
the obliquity of the mean luni-tidal spheroid is 
only equal to the hour-angle corresponding to that 
interval of time. 

8. We know, however, but little at present re- 
garding the actual time of the spring tides in dif- 
ferent parts of the ocean, and it is not even quite 
certain, although, as Airy remarks, it is extremely 
probable, that in the southern seas they take place 
at an interval after the full and change, although it 
may be at a less interval than on the Atlantic coast 
of Kurope. There must be observations on record 
(such as those of Sir Thomas Maclear at the Cape 

1 See Airy's Tides and Waves, 544. 


of Good Hope, which Staff-Commander Burdwood 
showed me in the Hydrographical Office of the 
Admiralty) valuable for determining this very im- 
portant element, for ports on all seas where any 
approach to a knowledge of the laws of the tides 
has been made. 

To collect information on this point from all 
parts of the world will be one of the most interest- 
ing parts of the work of the Committee. 

9. Another very interesting subject for inquiry is 
the lunar fortnightly, or solar semiannual, tide, the 
determination of which will form part of the com- 
plete harmonic reduction of proper observations 
made for a sufficient time. The amounts of these 
tides must be very sensible in all places remote 
from the zero line l of either northern or southern 
hemisphere ; unless the solid earth yields very 
sensibly in its figure to the tide-generating force. 2 
Thus it has been calculated that if the earth were 
perfectly rigid, the sum of the rise from lowest to 
highest at TenerifTe, and simultaneous fall from 
highest to lowest at Iceland, in the lunar fort- 
nightly tides, would amount to 4*5 inches. The 
preliminary trials of plans for harmonic reduction 
referred to below, make it almost certain that 
hourly observations, continued for a month at two 
such stations as these, would determine the amount 
of the fortnightly tide to a fraction of an inch, in 

1 Thomson and Tait's Natural Philosophy, 810. 

2 See Appendix A (3) above. 

THE TIDES. (APP. >.) 221 

ordinarily favourable circumstances as to barometric 
disturbance, and so would give immediate data for 
answering, to some degree of accuracy, the question 
how much does the solid earth really yield to the 
tide-generating force ? 

10. A year before proposing to Section A of the 
British Association the appointment of a Com- 
mittee . to promote tidal investigation, I applied 
through my friend Staff-Commander Moriarty, 
R.N., for a year's tidal diagrams of any trustworthy 
tide-gauge ; and, through his kind assistance, 
I accordingly received from Staff-Commander 
Burdwood, R.N., those of the Royal Harbour of 
Ramsgate for 1864. From the beginning of last 
winter till the present time I have been engaged 
in the reduction of these observations, chiefly 
assisted by Mr. Ebenezer Maclean, but also by 
Mr. James Smith and Mr. William Ross, students 
of the Natural-Philosophy Class of Glasgow Uni- 
versity, last Session, who volunteered to perform 
the laborious processes of measurement and calcu- 
lation required. The heights above a certain point 
near the bottom of the scale, chosen to avoid 
negative quantities, were measured from the 
diagrams for noon and midnight 6 P.M. and A.M., 
3 P.M. and A.M., 9 A.M. and P.M. ; but after some 
preliminary calculations had shown what valuable 
results might be expected, the measurement was 
made for every mean solar hour of the year, and 
the numbers written down in a book, with a page 


for each day. Certain averagings of these results, 
arranged in proper groups, were then made, and 
somewhat closely approximate determinations of 
the amplitude and epoch of the solar semidiurnal 
and lunar semidiurnal tides were deduced. I 
also found very decided indications of an annual 
rise and fall, which seemed to exceed the amount 
of the solar semidiurnal tide, and to make the 
mean level very sensibly higher in autumn than in 
spring, an effect probably to be accounted for by 
an annual period in the amount of water received 
into the sea by drainage and the melting of ice, 
and from the direct fall of rain into it. With 
these indications of what might be expected from 
a thorough reduction of tidal observations accord- 
ing to the harmonic plan, I felt justified in bring- 
ing the subject before the British Association and 
proposing that the co-operation of a Committee 
should be invited, and a grant of money made to 
defray expenses which might be found necessary 
for carrying on the several parts of the investiga- 
tion proposed. Acting on the advice of the 
Astronomer-Royal, I have put the work of con- 
tinuing the computations for the Ramsgate ob- 
servations into the hands of a skilled calculator, 
Mr. E. Roberts, recommended to me by Mr. Farley 
of the Nautical Almanac Office, for this purpose. 
With his very able assistance I hope soon to have 
the harmonic analysis completed for the year's 
observations now in his hands ; and I shall lose as 

THE TIDES. (APP. D.} 223 

little time as possible in communicating the results 
to the Committee. I shall keep in view the trial 
(with which I commenced work on these observa- 
tions) to find how much of valuable results can be 
obtained from a comparatively small number of 
observations, for instance, observations every three 
hours of the twenty-four, instead of every hour, or 
every three hours of the day half of the twenty- 
four, for the purpose of learning how to reduce, as 
far as possible, the labour and inconvenience im- 
posed upon those to whom may be committed the 
execution of observations taken in future according 
to advice from this Committee. 

II. Probably the best personal observations that 
have ever been made on the tides are those de- 
scribed by Captain Sir James Clark Ross, R.N., in 
the Philosophical Transactions for June, 1854, as 
having been made by the officers and petty officers 
of H.M. ships Enterprise and Investigator, every 
hour of the twenty-four, for nine months, com- 
mencing November 1st, 1848, in Port Leopold. 
A full harmonic reduction of these observations, 
and of the simultaneously observed heights of the 
barometer, must, as early as possible, be executed 
by this Committee. 1 

1 This has been performed, and the results have been published 
in the Report of the British Association, for 1876, p. 289. 



{Thomson and Taifs " Natural Philosophy? 804870.] 

IF we suppose the moon to be divided into two 
halves, and these to be fixed on opposite sides of 
the earth, at distances each equal to the true moon's 
mean distance : the ellipticity of the disturbed 
terrestrial water-level would be 3/(2 x 60 x 300000) 
or 1/12,000,000; and the whole difference of levels 
from highest to lowest would be about if feet. 

The rise and fall of water at any point of the 
earth's surface we may now imagine to be produced 
by making these two disturbing bodies (moon and 
anti-moon, as we may call them for brevity) revolve 
round the earth's axis once in the lunar twenty-four 
hours, with the line joining them always inclined to 
the earth's equator at an angle equal to the moon's 
declination. If we assume that at each moment 
the condition of hydrostatic equilibrium is fulfilled, 
that is, that the free liquid surface is perpendicular 
to the resultant force, we have what is called the 
" equilibrium theory of the tides." 

But even on this equilibrium theory, the rise and 
fall at any place would be most falsely estimated if 
we were to take it, as we believe it is generally 

THE TIDES. (APP. E.) 225 

taken, as the rise and fall of the spheroidal surface 
that would bound the water were there no dry land 
(uncovered solid). To illustrate this statement, let 
us imagine the ocean to consist of two circular 
lakes, A and B, with their centres 90 asunder, on 
the equator, communicating with one another by a 
narrow channel. In the course of the lunar twelve 
hours the level of lake A would rise and fall, and 
that of lake B would simultaneously fall and rise to 
maximum deviations from the mean level. If the 
areas of the two lakes were equal, their tides would 
be equal, and would amount in each to about 7/8 of 
a foot above and below the mean level ; but not so 
if the areas were unequal. Thus, if the diameter of 
the greater be but a small part of the earth's qua- 
drant, not more, let us say, than 20, the amounts 
of the rise and fall in the two lakes will be inversely 
as their areas to a close degree of approximation. 
For instance, if the diameter of B be only i/io of 
the diameter of A, the rise and fall in A will be 
scarcely sensible ; while the level of B will rise and 
fall by about if feet above and below its mean ; 
just as the rise and fall of level in the open cistern 
of an ordinary barometer is but small in comparison 
with fall and rise in the tube. Or, if there be two 
large lakes, A, A', at opposite extremities of an 
equatorial diameter, two small ones, B, B', at two 
ends of the equatorial diameter perpendicular to 
that one, and two small lakes, C, C', at two ends of 
the polar axis, the largest of these being, however, 
VOL. in. Q 


still supposed to extend over only a small portion 
of the earth's curvature, and all the six lakes 
communicate with one another freely by canals or 
underground tunnels : there will be no sensible tides 
in the lakes A and A' ; in B and B' there will be 
high water of if feet above mean level when the 
moon or anti-moon is in the zenith, and low water 
of if feet below mean when the moon is rising 
or setting ; and at C and C' there will be tides 
rising and falling 7/8 of a foot above and below the 
mean, the time of low water being when the moon 
or anti-moon is in the meridian of A, and of high 
water when they are on the horizon of A. The 
simplest way of viewing the case for the extreme 
circumstances we have now supposed is, first, to 
consider the spheroidal surface that would bound 
the water at any moment if there were no dry land, 
and then to imagine this whole surface lowered or 
elevated all round by the amount required to keep 
the height at A and A' invariable. Or, if there be 
a large lake A in any part of the earth, communi- 
cating by canals with small lakes over various parts 
of the surface, having in all but a small area of 
water in comparison with that of A, the tides in any 
of these will be found by drawing a spheroidal 
surface of if feet difference between greatest and 
least radius, and, without disturbing its centre, 
adding or subtracting from each radius such a 
length, the same for all, as shall do away with rise 
or fall at A. 

THE TIDES. (A PP. E.) 227 

It is, however, only on the extreme supposition 
we have made, of one water area much larger than 
all the others taken together, but yet itself covering 
only a small part of the earth's curvature, that the 
rise and fall can be done away with nearly altogether 
in one place, and doubled in another place. 

Q 2 


\_Taken from ''''Good Words" 1874 and 1879; an d United 
Service Institution Lectures, 1878 and 1880.] 

HUMAN in- 
ventions have 
grown by Evo- 
lutioji. Of per- 
haps no other 
than the Mari- 
ner's Compass 
can it be said 

that it came into existence complete in a 
moment. The person who first having a piece 
of loadstone or a magnet, so supported as 


to be movable round a vertical axis, perceived it 
to turn into one particular direction when left 
to itself, and who found that the positions thus 
assumed were sensibly parallel when the sus- 
pended magnet is carried about to different 
places indoors or out-of-doors, near enough to 
be within sight of one another, invented the 
Mariner's Compass. There may have been several 
independent inventors ; there can have been but 
one first inventor. The efforts of historical in- 
quirers have hitherto proved unavailing to fix 
either time, place, or person for this invention, 
not more remarkable for its definiteness as a 
discovery than for its perennial utility to the 
human race. 

It is generally believed that the compass was 
known at an early date in China, and used as a 
guide for travelling by land at a very early period 
of the world's history. In the English translation 
(London, 1736) of the Pere Duhalde's book on 
China, in the Section entitled Annals of the 
Chinese Monarchy r , a Chronological History of tJie 
most Remarkable Events that happened diiring the 


Reign of every Emperor, the following remark- 
able statement with reference to the Emperor 
Hoang Ti giving battle to Tchi Yeou occurs : 
" He, perceiving that thick fogs saved the enemy 
" from his pursuit, and that the soldiers rambled 
" out of the way, and lost the course of the wind, 
" made a carr which show'd 'em the four cardinal 
" points ; by this method he overtook Tchi Yeou, 
u made him prisoner and put him to death. Some 
" say there were engraved in this carr, on a plate 
" the characters of a rat and a horse, and under- 
" neath was placed a needle, to determine the four 
" parts of the world. This would amount to the 
" use of the compass, or something very near it, 
" being of great antiquity, and well attested. 'Tis 
" pity this contrivance is not explained, but the 
" interpreters knowing only the bare fact dare not 
" venture on conjectures." 

Hoang Ti was the third Emperor. The first 
date given in Duhalde's Annals is that of the 
death of the eighth Emperor Yao, 2277 years 
before the Christian era ; and it is stated that the 
number of years from the time of Fohi, founder 


of the dynasty, and first Emperor, till the beginning 
of Yao's reign is very doubtful. Assuming the 
date of Yao's death to be correct, we may safely 
conclude that Hoang Ti must have lived some 
time about 2400 or at the latest 2350 years before 
the Christian era. Duhalde's work was founded on 
narratives written by French Jesuit missionaries 
who lived in China during the latter part of the 
seventeenth century, and before publication was 
most scrupulously revised and corrected, when 
necessary, by the Pere Contancin, who had spent 
thirty-two years in China. It is impossible to 
doubt but that the narrative represents accurately 
the traditions current in China at that time. 
The instrument which the Emperor Hoang Ti is said 
to have used cannot possibly have been anything but 
a compass, as nothing else could have done what 
it is said to have done. It is then perfectly cer- 
tain that at the time when the quoted tradition 
originated, the Compass was known in China. 
We have thus irrefragable evidence that the com- 
pass was known at a very early time in China, and 
fairly strong evidence for believing it to have been 


known there as early as 2400 years before the 
Christian era. 

The directive quality of the magnet, which 
constitutes the essence of the mariner's compass, 
was not known to the Greeks and Romans ; for in 
the writings of Homer, Theophrastus, Plato, 
Aristotle, Lucretius, and Pliny, we find abundant 
evidence of knowledge of all the other ordinary 
magnetic phenomena, but not a trace of any know- 
ledge of this most marked property. It is clear that 
of all those writers, or of the observers and experi- 
menters on whom they had depended for infor- 
mation, not one had ever supported a piece of 
loadstone, or of magnetized steel, in such a manner 
as to leave it free to turn round horizontally : or 
that if any one of them had ever done so, he was 
remarkably deficient in perceptive faculty. 

The earliest trace we now have of the mariner's 
compass in Europe is contained, according to 
Professor Hansteen (Inquiries Concerning tJie 
Magnetism of the Earth ), in an account of the 
discovery of Iceland by the Norwegian historian 
Ara Frode, who is cited as authority for the fol- 


lowing statement : " Flocke Vilgerdersen, a re- 
" nowned viking, the third discoverer of the island, 
" departed from Rcgaland in Norway to seek 
" Gadersholm (Iceland), some time in the year 868. 
"He took with him three ravens to serve as guides ; 
" and in order to consecrate them to his purpose 
" he offered up a great sacrifice in Smarsund, 
" where his ship lay ready to sail ; for in those times 
" seamen had no loadstone (leidarstein) in the 
" northern countries. In Icelandic, Leid signifies 
" region, and on this account the polestar is named 
" Leidstjerna, consequently Leidarstein signifies 
"guiding-stone. According to the testimony of 
" Snarro Sturleson, Are Frode was born in the year 
" 1068. This account was therefore probably 
" written about the end of the eleventh century." 

We have thus very strong evidence that the 
mariner's compass became known in the northern 
countries of Europe between the years 868 and 
1 100. We have distinct evidences from several 
different sources that the mariner's compass came 
to be pretty generally known through Europe in 
the thirteenth century. A poem by Guiot 


of Provence, entitled La Bible Guiot, forming a 
quarto manuscript of the thirteenth century, on vel- 
lum, belonging to the Bibliotheque du Roi at Paris, 
contains a description of the mariner's compass 
and of its employment by sailors, so curious and 
interesting that it is quoted in almost every 
historical sketch of magnetism. The following 
verbatim copy of the old French, followed by a 
literal English translation, of Guiot's statement 
regarding the compass, is taken from Barlow's 

" Treatise on Magnetism " in the Encyclopedia 
Metropolitana : 

Icelle estoile ne se muet 
Une arts font qui mentir ne puet 
Par la vertue de la Manete 
Une piere laide et brunete 
Ou il fers volenters se joint 
Ont regardent lor droit point 
Puez c'une aguile lont touchie 
Et en un festue lont fishie 
En longue-la mette sens plus 
Et il festui la tient desus 
Puis se torne la point toute 
Centre lestoile sans doute 
Quant il nuis est tenebre et brune 
Con ne voit estoile ne lune 
Lor font a laguille alumer. 


Puiz ne puent ils assorer 
Contre lestoile vers le pointe 
Par se sont il mariner cointe 
De la droite voie terns 
C'est uns ars qui ne puet mentir. 


This same star does not move, and 

They (the mariners) have an art which cannot deceive, 

By the virtue of the magnet, 

An ugly brownish stone, 

To which iron adheres of its own accord. 

Then they look for the right point, 

And when they have touched a needle (on it) 

And fixed it on a bit of straw, 

Lengthwise in the middle, without more, 

And the straw keeps it above ; 

Then the point turns just 

Against the star undoubtedly. 

When the night is dark and gloomy 

That you can see neither star nor moon, 

Then they bring a light to the needle, 

Can they not then assure themselves 

Of the situation of the star towards the point ? 

By this the mariner is enabled 

To keep the proper course ; 

This is an art which cannot deceive. 

In this passage, the words, "and the straw keeps 
it above," imply undoubtedly that the needle was 
to be floated in water by the straw. 


The experiment thus described by Guiot of 
Provence is familiar to the present generation, being 
taught by Peter Parley, The Boy's Own Book, 
and other eminent scientific instructors of the 
young : and any reader of Good Words, having 
access to a little bar magnet such as that used for 
attracting magnetic swans, may make it for himself. 
Guiot says " this is an art that cannot deceive," but 
I doubt whether any one repeating the experiment 
carefully will agree with him. The mode of 
support is not satisfactory. Water in an open 
basin scarcely ever has its surface free enough from 
dust or other impurities to allow a straw floating 
on it to turn with perfect freedom ; and it will be 
found that the needle will sometimes stick in 
positions sensibly inclined to one definite line 
towards which it tends, or at best that it will come 
very sluggishly into its proper position. A pretty 
and instructive experiment may, however, be made 
by deviating a little from the ordinary way of 
floating the needle. Instead of placing it length- 
wise on a straw, stick it transversely through one 
end of a small round wooden bar. The smooth 


round stem of a fine kind of wooden lucifer match, 
sometimes met with, answers very well, the head 
with the inflammable substance being of course cut 
off; but the stem of an ordinary match may be 
taken, one end of it slightly flattened to allow the 
needle to be pressed through it easily, and the 
whole thinned away so much that it will just 
barely float the needle. The needle must be ad- 

FlG. 31. 

justed so that it will rest horizontally with the 
wooden bar vertical over it. The bar ought to be 
longer than half the length of the needle, otherwise 
there is a difficulty in preventing one end or other 
of the needle from rising to the surface of the 
water. If the bar is seen to project even so much 
as one-tenth of an inch above the surface of the 
water, it should be cut shorter ; and the part of it 


at the surface of the water, when finally adjusted, 
ought to be nicely rounded. After completing 
this adjustment, which may require a little patience, 
pull the needle out from the wooden stem, and 

FIG. 32. 

steady it upon a table by aid of two fingers. 
Draw one end of the bar magnet once along it 
steadily from eye to point. Replace the needle 
in its proper position on the wooden stem and 
float it. It will then be seen to turn into a position 


not very much different from the true north and 
south line (unless the experiment be made far 
north in North America, or far south in the 
Antarctic regions). If turned out of this position 
and left to itself again and again, it will turn again 
and again into the same position, and always with 
the eye and point similarly situated as to north 
and south. Suppose, for example, the eye turns 
to the north and the point to the south. Remove 
the needle again, and go through the same opera- 
tion as before, several times running. Replace it 
in its floater, and it will be found to turn decidedly 
faster into the north and south line than before. 
Again take out the needle and go through the 
same operation, only with the other end of the bar 
magnet from that first employed. Replace it on 
its floater. You will now find it turning much less 
rapidly into its former position, or possibly turning 
into the reverse position. Take it out, and repeat 
several times the last operation, with the bar 
magnet. After having done this a sufficient 
number of times, you will find the needle turning 
its point to the north and its eye to the south. Or 


again, the magnetism once given by the little 
magnet may be reversed by drawing the same end 
of the same bar-magnet in the contrary direction a 
sufficient number of times along the needle. If, 
however, the needle has been magnetized by a 
more powerful magnet, it may be found difficult or 
impossible to reverse its magnetism by the simple 
operation described above. A convenient way of 
testing the direction shown by the needle, is to 
draw a black line on a piece of white paper, and 
place it below the tumbler or finger-glass. Turn 
the paper round until the needle, resting in the 
centre of the glass, is seen to be exactly over the 
line. Deflect the needle from this position again 
and again, and you will find it always coming with 
great accuracy to the same line. 

Dr. Gilbert of Colchester, Physician in ordinary 
to Queen Elizabeth, discovered the true explana- 
tion of this wonderful phenomena to be that the 
earth acts as a great magnet upon the movable 
needle, and thus founded the science of terrestrial 
magnetism. But an explanation of this discovery 
must be reserved for a continuation of the present 


article. In the meantime, any reader who is 
sufficiently interested may experiment for himself 
upon the mutual influence between the bar-magnet 
and the floating needle, and between two needles 
separately magnetized and floated. He may even 
readily enough anticipate Gilbert's discovery, and 
particularly his reasons for marking the poles N 
and S in the manner illustrated in the preceding 
sketch, which is at variance with the rule un- 
happily still followed by British instrument-makers, 
notwithstanding Gilbert's strong and early re- 
monstrance against it 

The first part of this article was written five 
years ago. I then thought I had a pleasant and 
easy task before me in the completion of it to 
describe a scientific instrument which was known 
to the Chinese two thousand years before the dawn 
of science, and first used by them as a guide across 
the deserts of North-Eastern Asia ; which for six 
hundred years has been in regular use by European 
mariners as a guide at sea ; and which is now of 
ancient and world-wide renown as an appropriation 
from the most recondite province of modern 
VOL. in. R 


physical science to purposes of great practical 
utility to mankind. (It is worthy of remark, in 
passing, that there are just two other practical 
applications of electro-magnetic science extensively 
in use at the present day the electric telegraph 
and electro-plating. These two upstarts, neither 
of them fifty years old, are both to-day familiar in 
every British household, while the venerable old 
mariner's compass, popular as it is in name, is not 
much more popularly known, in reality, now, than 
when Guiot of Provence described it six hundred 
years ago as pointing to "the star," or when 
Shakespeare made " lode-star " a symbol of attrac- 
tion.) But when I tried to write on the mariner's 
compass, I found that I did not know nearly 
enough about it. So I had to learn my subject. 
I have been learning it these five years, and still 
feel insufficiently prepared to enlighten the readers 
of Good Words upon it when I now resume the 
attempt to complete my old article. 

In the slight historical sketch of the mariner's 
compass which appeared in Good Words it was 
pointed out that Dr. Gilbert, of Colchester, 


Physician in ordinary to Queen Elizabeth, dis- 
covered the true explanation of the wonderful 
directional tendency manifested by magnetized 
needles. His explanation is, that the earth, not 
the pole-star, or any other " lode-star," but the earth, 
acts upon a movable needle, as does a lump of 
lode-stone or a bar magnet, held anywhere in its 
neighbourhood. To illustrate Gilbert's discovery 
I described a simple mode of experimenting, by 
which any one sufficiently interested may find for 
himself the mutual influence between two magnets, 
and suggested a mode of supporting the needle by 
flotation, to give it mobility, as this was interesting 
in connection with the earliest known European 
account of the mariner's compass, that of Guiot of 
Provence, which describes the needle as being 
floated on a straw in a basin of water. If a sewing 
needle be hung by a fine thread tied round its 
middle, it will have freedom of motion enough to 
let any one verify for himself, without the trouble 
of floating it, that two needles similarly magnetized 
by the use of a little toy magnet (bar or horse-shoe), 
act upon one another with repulsion between ends 

R 2 


which were similarly dealt with in the process of 
magnetization, and with attraction between ends 
which were dissimilarly dealt with. When one end of 
the needle turns in virtue of its magnetism towards 
the earth's northern regions, its magnetic quality 
is, therefore, dissimilar to that of the earth's northern 
regions, and similar to that of the earth's southern 
regions : therefore the end of the needle which 
when there is freedom to turn, turns towards the 
northern regions of the earth, has magnetism o f 
the same name as that of the earth's southern 
regions, and the end of the needle which is repelled 
from the north has the same kind of polarity as 
that of the earth's northern regions. Hence Gilbert 
remarks that that end of the needle which points 
from the north has truly northern polarity p , and the 
other end, which points towards the north, has truly 
southern polarity. And he complains that all 
writers and instrument-makers and sailors, up to 
his time, had erroneously estimated as the north- 
pole of the lodestone or steel the point of it that is 
drawn to the north and the south pole the point 
that is drawn to the south. 


Much confusion, and much of the difficulty now 
felt by practical men in understanding the elements 
of magnetism, has arisen through British instru- 
ment-makers having persisted up to the present 
day in this evil usage, notwithstanding Gilbert's 
strong remonstrance against it two hundred years 
ago. It is no doubt proper to mark on the fly-card 
of the compass the letters N. and S. at the points 
which are directed towards the north and towards 
the south, just as the letters E. and W. and N.E 
and N.W. are marked on the card, to show the east 
and west and north-east and north-west directions ; 
and thus no confusion can arise as to the indica- 
tions of the mariner's compass. But when a needle 
or a bar of steel has letters N. and S. marked on its 
ends to show its magnetism, N. ought to show true 
North magnetism and S. true South. 

Gilbert gave his discovery of Terrestrial 
Magnetism to the world in a Latin quarto volume 
of 240 pages, printed in London in the year 1600, 
three years before his death. A second edition ap- 
peared at Stettin twenty-eight years later, edited by 
Lochman, and embellished with a curious title-page 


in the form of a monument, ornamented with com- 
memorative illustrations of Gilbert's theory and 
experiments, and a fantastic indication of the 
earliest European mariner's compass, a floated 
lode-stone, but floating in a bowl on the sea and 
left behind by the ship sailing away from it. 

In the upper left-hand corner is to be seen 
Gilbert's terella and orbis virtutis. The terella is a 
little globe of lode-stone, which he made to illustrate 
his idea that the earth is a great globular magnet. 
Terellas have been made for the illustration of mag- 
netic principles by the philosophical instrument- 
makers ever since Gilbert's time, and specimens arc 
to be found probably in every old collection oi 
physical lecture apparatus. The orbis virtutis is 
simply Gilbert's expression for what Faraday called 
the field of force, that is to say, the space round a 
magnet, in which magnetic force is sensibly exerted 
on another magnet, as, for instance, a small needle, 
properly placed for the test. Gilbert's word virtue 
expresses even more clearly than Faraday's word 
force the idea urged so finely by Faraday, and 
proved so validly by his magneto-optic experiment, 


that there is a real physical action of a magnet 
through all the space round it though no other 
magnet be there to experience force and show its 
effects. The meaning of the little bars bordering 
the terella in Lochman's frontispiece is explained 
near the beginning of Gilbert's book (Lib. I. Cap. 

FIG. 33- 

iii.), where he describes a very fine iron wire, "of 
the length of a grain of barley," placed upon a 
terella and standing erect from the surface at either 
of two points, which he calls poles, but taking ob- 
lique positions at other points, and lying flat at any 
point of a circle midway between the two poles. 


The smallness of the magnetic indicator here allows 
the magnetic force to show its effect with compara- 
tively little disturbance from gravity. The nature 
of the magnetic action of the terella is further illus- 
trated by Gilbert in the annexed diagram (Fig. 33), 
reproduced in facsimile from his original edition. 1 
It represents the directions taken by a small 
magnetized steel needle, supported by a cap on a 
finely pointed stem, at different positions in the 
neighbourhood of a terella. The same results 
are shown more completely and more accurately 
by the diagram of curves shown in Fig. 34, 
which have been calculated mathematically from 
the laws of magnetic force discovered by Coulomb 

1 In page 14 of Lochman's edition there is a curious error in 
this diagram, which is repeated in page 80, the needle in the 
equatorial position being shown with the arrow-head intended to 
denote its true south pole turned towards the south instead of 
towards the north of the terella. Lochman's wood-engraver 
generally reversed Gilbert's diagrams as to right and left (giving, 
for example, a remarkable picture of a blacksmith wielding with 
his left hand a hammer to strike a piece of iron on the anvil, as a 
reproduction of Gilbert's picture which shows a blacksmith working 
with his right arm), and seems to have corrected the reversal for 
two of the needles, and omitted to do so for the other, in his 
diagrams of the terella. 


two hundred years after Gilbert's time. A very 
small magnetized needle, pivoted so as to be per- 
fectly free to turn about its centre of gravity any- 
where in the neighbourhood of a terella, will place 
its length exactly in the direction of the curves of 
the diagram through it or beside it, with its poles 
in the positions marked by the arrow (feather for 
true north pole, and point for true south). 

Gilbert uses the results of his observations on the 
direction of a small needle in the neighbourhood of 
a terella to explain both the horizontal direction 
indicated by the mariner's compass in different 
parts of the earth, which had been known for 
thousands of years, and the " dip," discovered by 
Robert Norman, sailor and nautical instrument- 
maker, a quarter of a century before the publication 
of Gilbert's book. Imagine the terella of the 
diagrams to be not a terella, but the earth itself, 
and by looking at the diagrams you will have, from 
the one showing curved lines of force, a clear idea 
of the general character of the directional tendency 
exhibited by a needle anywhere at the earth's sur- 
face, or which would be exhibited by a needle 


removed to thousands of miles from the earth. In 
experiments with a terella the needle is attracted 
obliquely or directly towards the globe with a very 
perceptible force. This is because the length of the 
needle is so considerable in proportion to the 
diameter of the globe that the magnetic forces on its 
two ends are not equal and parallel. But the 
length of the largest of mariner's compass needles 
is not more than about -4 oWo-<rs-o> an d the length of 
the largest bar magnet that has ever been suspended 
so as to show by its movements any motive ten- 
dency it may experience from the force of terrestrial 
magnetism is not more than 1 ^ -, of the earth's 
diameter, and therefore magnetic needles or bar 
magnets experimented on in any part of the world 
experience as wholes no sensible attraction towards, 
or repulsion from, the earth, and show only a direc- 
tional tendency according to which a certain line 
of the magnet called its magnetic axis takes the 
direction indicated by the curved lines of force in 
our diagram. The word pole has been much used, 
but somewhat vaguely, to express a point in, or 
near, the surface of a body where there seems some- 


thing like a concentration of magnetic action. In 
respect to bar magnets, or magnetic needles, I shall 

FIG. 34. Curved lines of force. 

use the term " north pole " in a perfectly definite 
sense to signify a certain " centre of gravity " of 
northern polarity, and the term " south pole " to 


signify similarly a " centre of gravity " of southern 
polarity. Thus the action of terrestrial magnetism 
on a bar magnet is very rigorously the same 
as that of two forces in dissimilar directions in 
parallel lines through the two poles, as illustrated 
in the annexed diagram ; and the result, when 
the bar is free to turn, is that it can only rest 

FIG. 35. 

with the line joining its poles in the direction of 
the lines of force. 

Gilbert, in respect to his terella, uses the word 
pole definitely, to denote either point in which the 
little indicating needle places itself perpendicular to 
the surface ; and in this perfectly definite sense the 
word " pole " is used in the modern science of 
terrestrial magnetism. The north magnetic pole is 


the point of the earth's surface where the dipping- 
needle rests with its magnetic axis vertical and its 
true south pole downwards ; the south magnetic 
pole is the point where the dipping-needle rests with 
its axis vertical and its true north pole downwards. 
The line of no dip, or that line round the earth at 
every point of which the dipping-needle is hori- 
zontal, is called the magnetic equator. At either 
pole a horizontal needle, supported so as to be free 
to turn round a vertical axis, shows no directive 
tendency; thus the mariner's compass altogether 
fails at the magnetic poles, and for hundreds of 
miles round them shows but very feeble directional 

Gilbert fell into one grand error by a dereliction 
from his own principles of philosophy. He as- 
sumed, without proof from observation, that the 
earth's magnetic poles must concide with the " poles 
of the world," as he calls those points which we 
nowadays call the true astronomical poles, to dis- 
tinguish them from the magnetic poles, being, in 
fact, the points in which the earth's surface is cut 
by its axis of rotation. Modern Arctic and 


Antarctic explorations have shown the magnetic 
poles to be about 20 from the true poles. 

Shortly before Gilbert's time it had become 
known in Europe that there the needle did not 
point to true north, but several degrees to the 
east of true north, and not to the same number 
of degrees from the north in different places. The 
deviation of the needle from the true or astro- 
nomical north and south line was then called, and 
is called by sailors to the present day, the 
" variation " of the needle. Gilbert erroneously 
explained the different magnetic variations in 
different places by magnetic action of hills and 
headlands, and was thus led to the false conclusion 
that there would be no variation at great distances 
from the land or in the central parts of a great 
continent. We now know that the variation of the 
needle depends in the main on the fact that the 
magnetic axis of the earth deviates about twenty 
degrees from the axis of rotation, and that the 
amounts of the variation in different parts of the 
world are somewhat nearly as they would be if the 
distribution of terrestrial magnetism were regular 


as in a uniformly magnetized terella, but with its 
axis thus oblique to the axis of rotation. If this 
were exactly the case, the directions indicated by 
the compass would lie along great circles passing 
through the two magnetic poles, and the angles at 
which these circles cut the geographical meridians 
would be the actual variations in different parts of 
the earth, and the magnetic equator would be a 
circle on the earth's surface midway between the 
magnetic poles, inclined to the astronomical equator 
at an angle of 20. But, in fact, there are irregu- 
larities of distribution, such as those adduced by 
Gilbert to account for variation ; only we do not 
find them related to distributions of land and 
water, as he imagined. 

It is curious to find the idea of headlands attract- 
ing the compass still cropping up again and again 
two centuries after it was first suggested by Gilbert, 
and fifty or one hundred years after advances in 
knowledge of terrestrial magnetism had shown it 
to be erroneous. I find in an unpublished letter 
from the late Archibald Smith to Lord Cardwell, 
of date 1 3th of February, 1866, which has been 


communicated to me, the following statement re- 
ferring to the loss of the iron steamer Eastern 
Province r , lost on the south coast of Africa near 
Cape Agulhas, on the 26th of June, 1865 : " The 
captain attributed the loss to a change of the devia- 
tion of the compass, and that change to an attrac- 
tion of the coast, a cause to which sailors often 
attribute supposed irregularities of the compass on 
rounding a headland, irregularities which have 
never yet been shown to exist, and which I entirely 
disbelieve. It does not seem to have occurred to the 
captain or officers, or any one else, that a change 
of course is necessarily accompanied with a change 
of the deviation produced by the ship's iron." 

In the case of the Eastern Province it appeared 
from the captain's evidence laid before the com- 
mittee of inquiry held at Cape Town on the I4th of 
July, to investigate and report on the loss, that the 
ship had been steered on a compass course of N.W 
by N. till off Cape Agulhas, and then on N.N.W. 
which the captain supposed to be a change of 
course of one point, which would have carried her 
on a course parallel to the coast. Astronomical 


observation had shown an error (due, of course, to 
the iron of the ship) of 25 W. in the compass 
indication on the course on which they had been 
steering. If the amount of the error had been 
unaltered by the alteration of course, the change 
would have been one point, and the ship would not 
have gone ashore. Taking into account previous 
observations made in the ship, Smith found (by an 
application of the mathematical theory, which he 
had set forth in the Admiralty Compass Manual}, 
that the change of course actually made by the 
captain would probably diminish the deviation from 
25 to 18^, and showed that this change fully 
accounted for the error in the course which caused 
the loss of the ship. 

With reference to this old question the follow- 
ing statement by Captain Creak, describing obser- 
vations of unquestionable trustworthiness, is most 
interesting, and of great practical importance. It 
is extracted from his paper on the " Mariner's 
Compass in Modern Vessels of War," communi- 
cated to the Royal United Service Institution on 
the 3 ist of May, 1889. 



" The mariner's compass has yet another enemy 
" to contend with in the magnetic disturbance 
"caused by proximity to land. This reported 
" disturbing effect is not now brought forward as a 
" novelty, in fact it is an old story often told and 
" discredited by many whose opinions were well 
" worthy of consideration. Well-authenticated 
" reports of recent years show that both those 
" who doubted and those who reported were both 
" partly right and partly wrong. The facts are 
" these : it is seldom, if ever, that the visible land 
" disturbs the compasses of a ship, as her distance 
" from the shore would almost in every case 
" entirely keep her out of its magnetic influence. 
" It is the submerged land near the ship's bottom 
" which, possessed of magnetic properties, produces 
" the observed effects, sometimes of attraction, 
" sometimes of repulsion, on the north point of 
" the compass. 

" Now, I have brought this part of the subject 
" forward in order to place a clearly proved fact 
" on a proper basis, and not with the view of 
" alarming the seaman. We have now a list of 


" localities, situated in different parts of the world, 
>( where the disturbance of the compass has been 
" noted by trustworthy observers, and I would raise 
" a note of warning to navigators, prone to shave 
" corners on a dark night, guiding their ships solely 
" by the compass, that the rocks they approach 
" with ample water over them for the ship to float 
" and be safe, may be so strongly magnetic as to 
" deflect the compass, carrying the ship into serious 
" danger if not destruction. 

" Observations tend to show that magnetic rocks 
" in the northern hemisphere attract the north end 
" of the needle, and therefore a ship nearing the 
" land in moderate depths of water, say under 
" twenty fathoms, on northerly courses, would be 
" drawn nearer and nearer to them. In the 
" southern hemisphere the converse appears to 
" hold good, the north end of the needle being 
" generally repelled, and a ship steering on 
" southerly courses might be liable to close the 
" land without her officers knowing anything about 
" it. Two well-established examples of disturbing 
" localities will help to illustrate the foregoing 

S 2 


" remarks, which are the outcome of considerable 
" inquiry. 

" The first is the case of our surveying vessel 
" Meda, at Cossack, in North Australia. Here, 
" with the visible land three miles off, the Meda, 
" in eight fathoms of water, running on a line of 
" two objects on shore, had her compass steadily 
" deflected 30 for a quarter of an hour during 
" which she sailed over half a mile. 

" The next instance is that furnished by observa- 
" tions of the variation of the compass on the east 
" coast of Madagascar. The normal lines of the 
" variation for several miles of the coast from St. 
" Mary's Isle southward should be from about 
" 11 W. to 12 W.; but instead of this the French 
" men-of-war, which are frequently running up and 
" down this part of the coast, find that the varia- 
" tion near the shore at St. Mary's Isle is only 6 
" or 7 W. and 12 W. at 80' South : the north end 
" of the compass being repelled by the magnetic 
" properties of the bottom. These results are 
" analogous with those of observations on shore 
" in Madagascar, New Zealand, and other places." 


Captain Wharton, in the discussion following 
the reading of this paper, said : 

" Captain Creak has brought forward the ques- 
" tion of the disturbance of the compass on 
" approaching shore. For a long time it was 
" thought not possible that the compass could 
" really be disturbed. By well-known magnetic 
" laws the sphere of influence of any disturbing 
" forces is so small that it was thought quite im- 
" possible that the compass passing a point of 
" land should ever be disturbed by the magnetic 
" character of the rock. But in some extraordinary 
" manner it has been overlooked, that while a ship 
" is a long distance horizontally from land, she 
" may be passing very closely vertically over it 
" in shallow water, and it has only been recently 
" recognised that this is the true explanation, and 
" that there really is a danger in certain places, the 
" majority of which are quite unknown, in passing 
" over shallow water, of the compass being seriously 
" deflected. I believe now that it is known it will 
" be borne in mind." 

The statement regarding the Meda's observation 


and the 30 error of the compass, over so great a 
length of course as half a mile, is so startling that 
I wrote to Captain Creak, asking further parti- 
culars regarding it, and received from him the 
following in a reply of date March 29, 1890. 

" The circumstances were these 

" Approaching Cossack, North Australia, on 
"July 30, 1885, the commanding officer of the 
" Meda being sceptical of the reported * attraction 
" of the Island of Bezout, near the port of Cossack, 
" was on the look out to prove the non-existence 
" of the disturbance, when, four miles from Bezout, 
" in eleven fathoms, his compass was deflected two 
" points for a short time and then returned to its 
" proper direction. It being night the commander 
" was not convinced, but determined to look into 
" the matter under favourable circumstances. 

"September 17, 1885. The Meda steering 
" N.N.W. in very smooth water. Position by 
" angles made the ship to be N. 58 E. from Bezout, 
" distance three miles. Ship steered by a transit 
" of objects on shore in eight fathoms. The first 
" disturbance occurred when the bearing of Bezout 


"gradually changed to S. 53 W., then the bear- 
ing gradually altered to S. 63 W., S. 75 W., 
" and S. 89 W. This lasted for about a quarter 
" of an hour, ship's speed two knots. The bearing 
"then gradually returned to S. 58 W. All the 
" officers of the ship were on deck taking bearings 
" and angles. We were so struck by this that orders 
" were sent out for a more extended examination, 
" but the survey was broken up before the observa- 
" tions could be carried out. I have conversed 
" with the officers since, and they have no doubt 
" of the accuracy of their observation." 

" Although the observations were taken by care- 
" ful observers, on board a wooden vessel, the 
" results were so remarkable that further inquiry 
" and examination on the spot would have been 
" made had the vessel returned to the spot. It is 
" desirable that further observations should be 
" made, especially in a place where vessels approach- 
" ing the port all complain of the serious disturb- 
" ance to their compasses. They accuse Bezout 
" Island. I believe it to be a magnetic ridge under 
" the sear 


Captain Creak has also called my attention to 
the following statement in a paper which he 
read in 1886 before the Royal Society, " On Local 
Magnetic Disturbance in Islands situated far from 
a Continent " : 

" As an instance of large disturbance the results 
" obtained at the bluff, Bluff Harbour, in the South 
" Island, New Zealand, may be mentioned. In 
u 1857, during the land survey by the local govern- 
" ment officials, the following values of the declina- 
" tion were observed. 1 

On the summit of the bluff 6 54' E. 

30 feet north of the same position 9 36 W. 

west ., 5 04 E. 

east ,, 46 44 E. 

Normal from sea observations 16 20 E 

" On the summit of the bluff there was thus 
" shown to be a strong focus of red magnetism. 

" During the survey of the South Island by the 
" officers of H.M.S. Acheron, it was found necessary 
" to give up the use of compass-bearings at this 
" place, and adopt the plan of observing nothing 
" but true bearings." 

1 Transactions of New Zealand Institute, 1873, vol. vi., p. 7. 


" Supposing such a rock to be under water some 
" thirty or forty feet and a vessel passing near it, 
" one can conceive a greater deflection than 30. 
" Also that there may be ridges of rocks of much 
" greater extent, and of equal power to the bluff at 
" Bluff Harbour. In some parts of New Zealand 
" much larger deflections have been observed." 

Captain Creak also gives me the following 
extract from Transactions of New Zealand Insti- 
tute,. 1873, p. 7: 

"North of Port Chalmers the disturbing force 
" at many stations is very considerable. 

" At Highlay Hill the declination is 2 24' E. ; 
" in Hawksbury district, at Mount Watkins, it is 
" 3 W. ; and at Taieri Peak, a few miles to the 
" North, it is 104 47' E. In Moeraki district, at 
" trigonometrical station O, it is 26 10' E. ; and at 
" trigonometrical station P, it is only 50' E. 

" In Kauroo district, at Mount Difficulty, the 
" declination is i 02' W. ; at trigonometrical sta- 
" tion L., 13 30' E. ; at trigonometrical station S., 
22 E.; at Black Cap, 8 54' W. 

" These four stations are included within a radius 


" of about two and a quarter miles ; and lastly, the 
" declination at Kauroo Hill, about five miles N.E. 
"of Black Cap, is 41 3' E." 1 

In virtue of the irregularities of the distribution 
of terrestrial magnetism, rightly noticed by Gilbert, 
but wrongly attributed to magnetic continents, and 
mountains, and headlands, the lines of direction 
indicated by the compass are not great circles on 
the earth's surface, but somewhat irregular curves 
joining the north and south magnetic poles ; and 
the magnetic equator is not a circle, but a sinuous 
line round the earth. 

The best information regarding the configuration 
of these lines, at the present time, and generally 
regarding the present condition of the earth's 
magnetism, is to be found in the three small 
magnetic charts showing curves of equal variation, 
curves of equal dip, and curves of equal horizontal 
intensity, and in the large scale Admiralty 
Variation Chart, which have been prepared and 
reduced to the epoch of 1871 by Captain Evans, 

1 Such a country as this submerged to eight fathoms would 
trouble our compasses very considerably. CAPTAIN CREAK. 


C.B., R.N., and Lieutenant (now Captain) Creak, 
R.N., from the results of observation in all parts of 
the world, collected, analyzed, and exhibited, in 
fully detailed charts for the epoch of 1840 45, by- 
Sir Edward Sabine, R.A., K.C.B., in the Trans- 
actions of the Royal Society. 

The annexed diagrams (Fig. 36) of the northern 
and southern hemispheres are drawn according to in- 
formation taken from these charts. They exhibit, 
on a plan first proposed by the French navigator 
Duperrey, and largely used by Faraday in his 
drawings of lines ot magnetic force, the lines of 
direction of the mariner's compass in different parts 
of the world, referred to above. 

A traveller starting from any point of the earth's 
surface and travelling always along the line shown 
by the compass needle, and in the direction of the 
north point of the compass card, would be led to a 
certain point in the Island of Boothia, in about 
1 00 of west longitude, and 70 of north latitude. 
This point is the earth's north magnetic pole. Or, 
if he travels along the same line but in the contrary 
direction, that is to say in the direction of the south 


point of the compass card, he will be led to a point 
in about 146 of .east longitude, and 73 south 
latitude. This point is the earth's south magnetic 
pole. The diagram shows just two magnetic poles, 
and if, as is probably the case, it is approximately 
correct in the hitherto unexplored polar regions, 
Halley's celebrated hypothesis of four magnetic 
poles is disproved for the present time. But the 
dotted lines in the neighbourhood of the 
astronomical north and south poles are drawn 
conjecturally, and some degree of straining, 
particularly in the north polar region, is required 
to bring them all to pass through the points 
marked on the chart as the north and south 
magnetic poles. There is indeed a somewhat 
determined tendency of the lines in the explored 
regions of from 145 to 150 east longitude, to 
converge towards a point in the unexplored sea 
north of Siberia in about 105 east longitude, and 
80 north latitude, and it seems therefore not im- 
possible that there is in reality a north magnetic 
pole in that region. As for the points marked as 
north and south magnetic poles on the chart, the 



northern one was actually reached and passed by 
Parry and other Arctic navigators ; and the southern 
one was so nearly reached by Sir James Ross's Ant- 
arctic expedition of 1840 41, that there can be no 
doubt of there being a south magnetic pole not far 
from the position marked. But the question 
whether or not there are other poles, whether north 
or south, besides those marked cannot be quite 
decisively answered without more of observation, in 
the Arctic and Antarctic regions, than has hitherto 
been made. If there are really two north magnetic 
poles of convergence of the directional lines, there 
must, as shown by Gauss, be also a third pole, where 
the ordinary mariner's compass would show no 
directional tendency, and where the dipping needle 
would point with its true south pole vertically 
downwards. There would be no convergence of 
the directional lines to this intermediate pole, which 
might be called a pole of avoidance rather than a 
pole of convergence. 

Even should it turn out that there is only one 
north and one south magnetic pole now, it by no 
means follows that there may not have been at 


other times of the history of terrestrial magnetism 
more than two magnetic poles. Indeed, Halley 
had seemingly strong reason for inferring two 
north poles from observations of early navigators, 
showing large westerly variation of the compass in 
Hudson's Bay, and in Smith's Sound (longitude 80 
W., latitude 78 N.), and at sea in the north-west 
Atlantic ; at different times, from 1616 to 1682, 
when the compass in England was pointing due 
north (in the earlier part of the period a few 
degrees to the east of north, in the latter a few 
degrees to the west). It may be that the present 
tendency to converge to a point in the unexplored 
Siberian Arctic sea may be a relic of a north 
magnetic pole which existed in Halley's time and 
has since ceased to exist ; but the amount of trust- 
worthy information available scarcely suffices to 
justify such a conclusion. One thing is certain, the 
distribution of terrestrial magnetism has been 
changing ever since accurate observations were 
made upon it, and it is now enormously different 
from what it was in the year 1600. 

Observations of Gilbert's contemporaries served 


to bring to light for their successors, not for 
themselves, that great marvel of nature, the secular 
variation of terrestrial magnetism. Borough, Con- 
troller of the Navy of Queen Elizabeth, seems to 
have been the first to determine by accurate ob- 
servation the variation of the compass in England. 
He found it to be 11 15' to the east of north at 
London in 1580. It was then imagined to be 
essentially constant, and Gilbert obviously had not 
learned that it had changed when, in 1600, he 
reckoned its amount as about " half a point " (or 
5|). Twenty or thirty years after Gilbert's death 
observers began to notice that the variation had 
diminished considerably from the amount found for 
it by Borough. An accurate observation in 1633 
made the variation 4 5', so that it seemed to have 
diminished by 6 10' in the preceding fifty-three 

In 1659 the needle pointed due north in London ; 
in 1700 it pointed ioj to the west of north. 
From 1700 to 1818 the westerly variation continued 
increasing, but more and more slowly, till 1820, 
when at an extreme westerly variation of 24^ it 


turned, and began to come back from west towards 
the north, very slowly at first, and with gaining 
speed ever since, till now (1879) it has become 
reduced to 18 40', and is diminishing at the rate 
of nearly a fifth of a degree annually. 1 

From 1605 to 1609, at the Cape of Good Hope, 
the variation altered from half a degree east to 
one-fifth of a degree west, and from that time it has 
been becoming more and more westerly. The 
needle seems now, at the Cape of Good Hope, to 
be returning, or about to return, towards the north, 
and may probably enough again point due north 
there a few hundred years hence. 

Corresponding observations as to the magnetic 
dip have been made at different places. After the 
discovery of the dip by Robert Norman in 1576, 
when he found its amount in London to be 71 50', 
it increased gradually till about 1723, when it was 
74 42', and since that time it has been decreasing 
till it is now 67 36' ; and it is now decreasing 
about 2' annually. At the Cape of Good Hope 

1 [N T ote added August, 1890.] Since 1881 the rate of diminution 
of the westerly variation in London has become less than half what 
it was from 1879 to 1880. The variation in 1890 is 17 26' west. 



the dip (true north pole downwards) increased by 
11 in the hundred years from 1751 to 1851; it 
has been decreasing ever since, and is still steadily 

Besides these great changes in the distribution of 
terrestrial magnetism from century to century, 
there are small diurnal and annual fluctuations 
depending in some regular manner upon the sun's 
influence. It seems also that there are still smaller 
periodical fluctuations depending on the moon. 
Besides all these small periodic variations, the 
greatest of which does not amount to more than a 
small fraction of a degree in the direction whether 
of the compass or of the dipping-needle, or to 
more than a small fraction of one per cent, of the 
magnitude of the directing force, there are also the 
great irregular disturbances of terrestrial magnetism, 
called by Humboldt magnetic storms, amounting 
sometimes to as much as a degree or two on the 
direction, and to two or three per cent, on the 
magnitude, of the terrestrial magnetic force. A 
magnetic storm is never merely local, but is always 
experienced simultaneously over the whole earth 
and generally, perhaps always, at the same time 


brilliant displays of aurora are to be seen in 
northern and southern polar regions, often as far 
from either pole as our own latitudes, and some- 
times perhaps as far as the equator, and over both 
northern and southern hemispheres simultaneously. 
Though it is not quite certain that there is not 
always a display of aurora borealis or australis, or 
both, at the time of a magnetic storm, it is quite 
certain that no display of aurora, even of the 
faintest to be visible, is ever seen without marked 
disturbances of a delicately poised magnetic needle 
in any part of the world. 

The electric telegraph has made known to us 
another allied disturbance the underground 
electric storm which is found always to accompany 
the magnetic storm and auroral display. A fourth 
agency, atmospheric electricity, has its storms too ; 
and these produce great disturbances of the ordi- 
nary daily electric " earth current " discovered in 
every telegraph wire whether aerial or submarine. 

But though the thunderstorm produces dis- 
turbances of earth currents, and though disturbances 
of earth currents are also produced by some cause 
which produces also auroral displays and magnetic 

T 2 


storms, no connection, whether of simultaneous 
occurrence or of distinct physical relationship, has 
hitherto been discovered between thunderstorms 
and their accompanying earth currents on the one 
hand, and the common cause of auroral displays, 
magnetic storms, and the underground electric 
storms with which they also are accompanied. 

Still another wonder the sun-spots, and the ten 
and a half or eleven years' period of their alternate 
abundance and scantiness. It seems that in the 
years of most abundant sun-spots the magnetic 
storms have been greatly above average in 
frequency and in intensity ; and there have also 
been unusually brilliant and wide-spread auroral 
displays. The last year of maximum abundance 
of sun-spots, 1870, must be remembered by many 
of the readers of Good Words for brilliant 
auroral displays. The magnificent red aurora 
seen on several nights in the autumn of that year 
in the south of England, lighting up the sky as it 
might have been by burning cities, were connected 
in the popular imagination with the horrors of the 
Franco-German war raging at that time on the 
other side of the Channel. We are now coming 


again to a time of abundant sun-spots which, 
according to the period hitherto observed, should 
be about the year 1881 ; and if again there is an 
abundance of auroras and magnetic storms, there 
will be further confirmation of the hypothesis of 
physical connection between the dynamical cause 
of those grand solar atmospheric storms which 
produce we may even say which constitute the 
sun spots and the hitherto mysterious telluric 
influences concerned in our aerial auroras and un- 
derground earth currents and surface manifesta- 
tions of terrestrial magnetism. 

The mariner's compass consists essentially of a 
magnetized needle, or needles, supported in such 
a manner as to be free to turn round a vertical 
axis. The fanciful frontispiece to Lochman's 
edition of Gilbert's work, contains evidence of the 
manner of support used when the mariner's com- 
pass first became known in Europe, as recorded 
in Guiot de Provence's poem. 

The now ordinary method of support on a 
bearing-point and cap had probably been used by 
the Chinese several thousand years earlier, and in 


Europe, it had certainly become the practical 
method, both for land and sea compasses, long 
before Gilbert's time. In 1576 we find Robert 
Norman, an instrument-maker, balancing his 
needles and fly-card on a point, before the needles 
were magnetized ; then magnetizing the needles, 

and finding the card to balance, not in its previous 
horizontal position, but as represented in the dia- 
gram, with a slope downwards towards the north : 
and from this, being a philosopher as well as sailor 
and instrument-maker, he went on to the important 
scientific discovery of the dip. As for the 
mariner's compass, differing from the compass 


for use on land only in its gimballed bowl, here is 
Gilbert's description of it, a literal translation of 
the eighth chapter of his Fourth Book, entitled " On 
the Composition of the Nautical Compass in 
Ordinary Use, and on the Difference of Compasses 
of Different Nations." 

" In a round wooden bowl closed above with 
*' glass a pin fixed upright in the middle bears the 
*' fly-card. The glass cover protects the interior 
' against wind or any impulse of air from without, 
*' and at the same time allows the card and inner 
u lid of the bowl i.o be distinctly seen. The fly is 
'* circular and of light material, as cardboard. The 
u magnetized needles are fixed to it below. Its 
" upper side is divided into thirty-two spaces, com- 
'* monly called points, corresponding to that 
'' number of equal angular intervals of the horizon, 
" or of the winds, which are distinguished by 
" proper marks and a lily to mark the north point. 
' The bowl, \vith a lead weight attached to its 
'' bottom, hangs balanced horizontally in a brass 
%< ring, which, in a sufficiently complete compass, is. 
il transversely pivoted on another ring, this last 


" being attached to a proper stand, or ' binnacle/ 
" fixed in the ship ; thus the bowl levels itself to 
" the plane of the horizon though the ship is tossed 
" about in various directions by the waves. 

" The needles are either two with their ends 
" brought together, or one of nearly oval form with 
" pointed ends, which performs its duty more 
" surely and swiftly. 1 The attachment of the 
" needle, or needles, to the card circle is such that 
" its centre is in the middle of the magnetic iron ; 
" but, on account of the variation of the compass 
" from the meridian, artificers in different regions 
" and cities connect in different ways the needles 
" to the card in respect to their directions re- 
" latively to the thirty-two points. The first pre- 

1 This opinion of Gilbert's is not borne out by advanced know- 
ledge of the laws of magnetization, which show that the oval ring 
needle cannot be trusted to for keeping its magnetic axis securely 
in a constant direction under whatever disturbing influence it may 
be subjected to, as does a thin rod or bar. The oval form was 
authoritatively condemned on this account by the British Admiralty 
Committee of 1837, who found the theoretical objection amply 
confirmed by experience. They actually found compasses of this 
pattern, which had been in use for some time at sea, presenting 
errors of as much as three degrees on account of the displacement 
of the magnetization in the substance of the needle. 


" vails in the cities of the Mediterranean, in Sicily, 
" Genoa, and the Venetian Republic. In all those 
" places the magnetic iron is attached to the fly- 
" card with its length parallel to the diameter, 
" through the rose or lily, so that at any place 
" where there is no variation the true north and 
" south points are shown by this diameter of the 
" circle ; and where there is variation the amount 
" is shown by the deviation of the point marked 
" by the lily on the card from the true north. A 
" second prevails in Dantzic, throughout the Baltic 
" Sea, and in the Belgian provinces. In it the 
" needles are fixed three-quarters of a point to the 
" east of the lily. In Russia the difference 
" adopted is two-thirds of a point. Lastly, com- 
" passes which are made in Seville, Lisbon, 
" ' Rupella/ Bordeaux, Rouen, and anywhere in 
" England, have an interval of half a point between 
" the lily and the direction of the needles. 

" From those differences have grown up great 
" errors in nautical management and marine 
" science. For when the directional positions of 
" maritime places (as promontories, ports, islands) 


" are first found by means of the mariner's com- 
" pass, and when the height of the tide and times 
" of high-water have been found when the moon's 
" position was on this or that * point of the 
" compass ' (as they call it), it is incumbent to 
" inquire particularly in what region, or according 
" to the usage of what region, that particular 
" compass was made by which those directions of 
" places and those times of tides w r ere first 
" observed. For, any one who with a British 
" compass should follow tables of sailing directions 
" published for the Mediterranean Sea must be led 
" very far out of his straight course. So also, he 
" who in British, or German, or Baltic waters, uses an 
" Italian compass with the marine charts published 
" for those places, will often be led out of his right 
" way. Those differences in the compasses of 
" different places were made for the purpose of 
" avoiding error on account of the different vari- 
" ations in different parts of the world. Yet Peter 
" Nonius has sought for the meridian by the 
" mariner's compass or fly (versormm\ as the 
" Spaniards call the needle, taking no account of 


" the variation ; and he urges that there must be 
" none by many geometrical demonstrations on 
" foundations altogether vicious (on account of his 
" small knowledge and experience of magnetic 
" affairs). Likewise Peter of Medina, not admitting 
" the existence of variation, has deformed the 
" nautical art with many errors." 

The compass now in most common use at sea in 
all classes of ships of all nations is substantially the 
same as the compass made by Robert Norman 
three hundred years ago, and described as above 
by Gilbert. Happily now, however, all compasses 
are made according to the original Italian plan of 
marking the correct magnetic north direction by 
the lily, and thus we are now quite free from the 
gratuitous errors due to confusion as to the inten- 
tion of the instrument-maker so deservedly con- 
demned by Gilbert. 

The wooden bowl holds its place at the present 
day, not only in a few coasters and fishing boats, but 
in many old-fashioned sailing ships of high dignity. 
For the Admiralty standard compasses and for com- 
passes generally in merchant steamers, the bowls are 


now made of copper or brass, instead of wood. The 
lead weight and the gimbal-rings are in all com- 
passes just as described by Gilbert. The two 
varieties of needle which he describes the pointed 
oval needle and the pair of thin bent needles with 
their ends united made according to patterns 
which have survived without material change for 
at least three hundred years, are both still to be 
found at sea, though they have generally given way 
to safer and simpler forms recommended for the 
British Navy forty years ago by a scientific com- 
mittee appointed to examine the compasses then in 
use, and to advise regarding improvements. Accord- 
ing to the recommendation of this committee, the 
compass of the British Navy and of well-found 
merchant steamers has for its needles pairs of par- 
allel straight bars of flat clock-spring fixed below 
the card, with the breadth of the bar perpendicular 
to the card, instead of coinciding with the under 
surface of the card, as in the oval needles of the 
older compasses. In the Admiralty standard com- 
pass there are two pairs of needles ; in the compass 
of merchant ships, hitherto generally, just one pair 


attached to each card ; in the compass described 
below there are four pairs of comparatively very 
small needles. 

Instead of the mere paper or pasteboard 
described by Gilbert, a thin disc of mica, with 
paper pasted to it on each side is used for the fly- 
card, as rendering it less liable to warp. The cir- 
cumference of the circle is divided to degrees, and 
the thirty-two points of the ordinary compass are 
shown by bold marks a little inside the circle of 
degrees, as pictured in the reduced copy of a com- 
pass card at page 228. A jewelled cap fixed in the 
centre of the card bears the whole weight of the 
card and needles on a fine point of hardened steel 
or of a natural alloy of iridium and osmium (which 
is also used for the points of gold pens), being a 
substance much harder than steel, and not like 
steel liable to rust. 

The proper size for the compass card is a subject 
on which there has been great diversity of opinion 
and diversity of usage apparently from the begin- 
ning. Gilbert, in describing the azimuth compass 
of his own invention, specifies " at least a foot " as 


the diameter of the circle ; and this is still a 
favourite size of compass in large merchant ships. 
Compasses have been made as large as fourteen or 
fifteen inches, and as small as four or five inches 
for use on board sea-going ships. The Admiralty 
standard compass is only seven and a half inches 
in diameter, 1 and the steering compasses in the 
British Navy are generally still smaller. The 
practical experience of merchant sailors has led 
them to prefer larger sizes. Some of the great 
ocean steam navigation companies, after trying the 
Admiralty standard compass, and then the other 
extreme of fifteen-inch compasses, fell back upon 
ten inches. This is the size most commonly now 
in use for standard and azimuth compasses in 
preference to Gilbert's old size of twelve inches. 
Sailors naturally like the larger compass because 
it is more easily read at a distance, which, at all 
events for a steering compass, is a real practical 
advantage. Still, if the smaller compass worked 

1 [Note added June, 1890.] This was the case from about 1840 
till the end of 1889, when my ten-inch compass described below 
was adopted as the Admiralty standard compass. 


better it ought to be chosen, not only for azimuth 
or standard compasses, but also for the steering 
compass, on which immediately depends the 
straightness of the ship's course, a result of para- 
mount importance. But, in fact, taking compasses 
as ordinarily made hitherto, the smaller compasses 
do not work nearly so well as the larger. With 
similar care as to the bearing-point and cap, a ten- 
or twelve-inch compass, while more accurate or not 
less accurate in respect to error arising from friction 
on the bearing-point, is much steadier in a heavy 
sea than a compass of six or seven inches diameter ; 
and it is, in reality, practical experience of this 
advantage, not merely convenience of the larger 
card for reading azimuths on it or for steering by 
it, that has led to the general preference of ten- 
inch compasses in the British merchant service. 

The secret of the steadiness of a large compass 
is the longness of its vibrational period, and a small 
card would have the same steadiness as a large one 
if its vibrational period were the same. How little 
this is known is illustrated by the methods of pro- 
curing steadiness in common use. In some (as in 


the Admiralty " J " card, provided for use in stormy 
weather) there is a swelling in the middle of each 
of the steel needles to make them heavier ; in 
others heavy brass weights are attached to the 
compass cards as near the centre as may be, being 
sometimes, for instance, in the form of a small 
brass ring of about an inch and a half diameter. 
Another method, scarcely less scientific, is to blunt 
the bearing-point by grinding it or striking it with 
a hammer, as has not un frequently been done to 
render the compass " less lively ; " or to fill the cup 
with brickdust, as is reported by the Liverpool 
Compass Committee to have been once done 
at sea by a captain who was surprised to find 
afterwards that his compass could not be trusted 
within a couple of points. All these methods 
are founded on the idea that friction on the 
bearing-point is the cure for unsteadiness. In 
reality friction introduces a peculiar unsteadiness 
of a very serious kind, and is very ineffective 
in remedying the proper unsteadiness of which 
something is essential and inevitable in a com- 
pass on board a ship rolling in a heavy sea, and 


steering on any other course than due east or 
due west. 

It has generally been considered that the greater 
the magnetic moment 1 of the needles the better the 
compass ; it is not generally known that the greater 
the magnetic moment, other things the same, the 
more unsteady will the compass be when the ship is 
rolling on ocean wave slopes. 

Froude's theory of the rolling of ships, according 
to which he finds that the longer the vibrational 
period of the ship when set a-rolling in still water 
by men running from side to side, the steadier she 
will be in a seaway, is also applicable to the oscilla- 
tions of the compass produced by the rolling of the 
ship. The cause of these oscillations will be 
readily understood by looking at the diagram on 
page 290, which shows a magnetized needle hung 
by a single vertical thread. The arrow-head in the 
vertical line through its middle indicates the down- 
ward resultant force of its weight or gravity 

1 "Magnetic moment" is the proper expression for what in 
common language is often called "power," or "strength, ' of the 



through its centre of gravity. The other two arrow- 
heads indicate the " couple" of equal contrary 
forces of terrestrial magnetism in parallel lines 
through the centres of gravity of the northern and 
southern polarities of its two ends, in the oblique 
directions in which these forces are experienced in 
the north magnetic hemisphere. In virtue of this 

FIG. 38. 

magnetic couple, the needle would take an inclined 
position with true south pole down, and true north 
pole up (as represented in the diagram on page 
278), if the bearing-thread were precisely in the 
vertical through the centre of gravity. Hence 
that the needle may rest horizontally, the point of 
attachment of the thread must be a little on the 
northern side of the centre of gravity, as shown in 


the diagram ; and similarly we see that when the 
needle is supported by a cup on a point, as shown 
in subsequent diagrams, it will rest with the centre 
of gravity of the needle and fly-card a little to the 
south of the vertical through the bearing-point in 
the northern magnetic hemisphere, and a little to 
the north of this vertical in the southern magnetic 
hemisphere. Hence (except at the magnetic 
equator, where the needle rests with its centre of 
gravity exactly under the bearing-point), if the 
bearing-point be moved to and fro in the east and 
west horizontal direction, the centre of gravity of 
the card will tend to lag and again to shoot 
forward when the motion of the bearing-point is 
alternately being accelerated and being retarded. 
This is just what happens through the rolling of 
the ship when sailing on a north or south magnetic 
course, as the axis round which the ship is rolling 
is always below the position of the compass. The 
same action is experienced, though to a less degree, 
on any course not due east or due west. When a 
ship is sailing due east or due west, it is only 
through pitching that the needle can be thus 

U 2 


disturbed, but the disturbance due to this cause, 
except in a very small vessel, is scarcely 

There is also another cause of unsteadiness in 
which the rolling of the ship produces oscillations 
of the compass, and that is through what is called 
the heeling error. When the ship is inclined over 
to one side or other, the compass experiences a 
deflecting magnetic force tending to cause it to 
point in a different direction from that in which it 
points when the ship is upright. This influence, 
which sometimes amounts to as much as two 
degrees for every degree of heel, is, in many cases 
a more potent cause of unsteadiness than the 
merely dynamical influence of the ship's rolling ; 
and it is thus remarkable that, in many cases, the 
two influences conspire, each tending to draw, in the 
northern hemisphere, the north point of the compass 
card, and in the southern hemisphere, the south point 
of the compass card, to the upper side of the ship 
with maximum force when the inclination is a 
maximum ; and each is greatest when the ship's 
head is north or south, and nearly evanescent 


when east or west. A little later I shall have 
occasion to explain the magnetic appliance for cor- 
recting the heeling error, but when it is perfectly 
corrected there remains a true dynamical rolling 
error, which alone is enough both in wooden and 
iron vessels, sailing or steam, to keep the compass 
oscillating very wildly when the ship is rolling 
considerably in a sea-way. 

When the free vibrational period 1 of the compass 
card agrees with the period of the ship's rolling, a 
comparatively moderate degree of rolling may 
produce a great oscillation in the card. Now the 
longest period of actual rolling, to any considerable 
degree, in a sea-way is from fourteen to seventeen 
or eighteen seconds. The vibrational period of 
the " A" card of the Admiralty standard compass 
is, in this part of the world, about nineteen seconds, 
and that of the larger compass (ten-inch) of the 
merchant steamers about twenty-six seconds ; and 

1 The free vibrational period, or simply "the period" (as it 
may be called for brevity) of a compass, is the time it takes to 
perform a complete vibration to and fro, when deflected hori- 
zontally through any angle not exceeding 30 or 40, and left to 
itself to vibrate freely. 


it is certainly owing to the nearer agreement of the 
former than of the latter with the period of the 
ship's rolling, that in a heavy sea the Admiralty 
compass is more disturbed than the ten-inch 
compass in the merchant steamers. But to get 
satisfactory steadiness a much longer period still 
than the twenty-six seconds is necessary. Now, 
for the same weight and dimensions of compass 
card and needles, the smaller the magnetic moment 
of the needles' magnetism the longer will be the 
vibrational period. 

Hence, provided the bearing-point and cap be 
fine enough and smooth enough to obviate serious 
frictional error, greatness of magnetic moment 
is a disadvantage in respect to steadiness of the 
compass at sea. Smallness of magnetic moment 
is important for another reason, which is, that 
unless the magnetic moment be vastly smaller 
than that of any of the compasses ordinarily in use 
hitherto, the accuracy for all parts of the world, of 
the correction of what is called the quadrantal 
error in an iron ship, by the Astronomer-Royal's 
method (to be explained below), is vitiated by the 


inductive influence of the compass upon the iron 
correctors. Further, to allow the whole compass 
error in an iron ship to be really well corrected, 
without inconveniently or impracticably great 
magnets and masses of iron fixed at inconveniently 
great distances from the compass, the needles 
ought to be not only of less magnetic moment, but 
also much shorter than those in common use 
hitherto. The double problem, then, of obtaining 
a compass which shall be steadier at sea, and shall 
also be better adapted for the perfect correction of 
the error due to the iron of an iron ship, or of cargo 
carried by the ship, requires 

1. For steadiness a very long vibrational period 
with small frictional error. 

2. Short enough needles to allow the correction 
to be accurate on all courses of the ship for the 
place where the adjustment is made. 

3. Small enough magnetic moment of the 
needles to allow the correction of the quadrantal 
error to remain accurate to whatever part of the 
world the ship may go. 

This problem forced itself on me when I tried to 


write an article on the mariner's compass for 
Good Words five years ago, and hence it is that 
the article is not written until now. When there 
seemed a possibility of finding a compass which 
should fulfil the conditions of the problem, I felt 
it impossible to complacently describe compasses 
which perform their duty ill, or less well than 
might be, through not fulfilling these conditions. 
The accompanying diagram (Fig. 39) represents 
the solution at which I have arrived. Eight small 
needles of thin steel wire, from 3j inches to 2 
inches long, weighing in all 54 grains, are fixed 
(like the steps of a rope-ladder) on two parallel 
silk threads, and slung from a light aluminium 
circular rim of 10 inches diameter by four silk 
threads through eyes in the four ends of the 
outer pair of needles. The aluminium rim is 
connected by thirty-two stout silk threads, the 
spokes as it were of the wheel, with an aluminium 
disk about the size of a fourpenny-piece forming 
the nave. A small inverted cup, with sapphire 
crown and aluminium sides and projecting lip, 
fits through a hole in this disk and supports it 


by the lip ; the cup is borne by its sapphire 

FIG. 39. 

crown on a fine iridium point soldered to the 
top of a thin brass wire supported in a socket 


attached to the bottom of the compass bowl. 

The aluminium rim and thirty-two silk-thread 

- \ > .. 
spokes from a circular platform which bears a 

light circle of paper constituting the compass card 

Habitually, however, the whole movable piece 
which turns to the north, consisting of magnets, 
supporting frame-work, jewelled cap, and, in the 
ordinary compass, pasteboard or mica with paper 
pasted on it, is called for brevity the "card," or 
the "compass card." In the new compass the 
outer edge of the paper circle is notched and 
folded down along the outside of the aluminium 
rim ; pasted to tissue paper, with which the 
aluminium rim is firmly coated, so as to give a 
perfectly secure attachment ; and bound all round 
with narrow silk ribbon to prevent the paper 
from cracking off in any climate. For the sake 
of lightness a circle of 6 inches diameter is cut 
away from the middle of the paper, leaving an 
annular band, 2 inches broad, on which are 
engraved the points of the compass and a circle 
divided to degrees. 


The paper ring is cut across in thirty-two 
places, midway between the silk-thread spokes, to 
prevent it from warping the aluminium rim by the 
shrinkage it experiences when heated by the sun. 
Compass cards of the new kind made before this 
simple piece of engineering was applied to the 

FIG, 40. 

structure, used to be perfectly flat in cloudy 
weather at sea, and to become warped into a 
saddle-shape surface when the sun had shone 
brightly on them for a few minutes. Now with 
the radical cuts in the paper the compass may 
be first thoroughly moistened by the steam of a 


kettle, and then toasted before a hot fire, without 
in any sensible degree warping the aluminium 
rim or disturbing the degree or point divisions 
printed on the paper ; and in its proper place 
under glass in its bowl it remains quite undis- 
turbed through all variations of temperature 
from coldest weather to hottest sun in actual 

The entire weight of the card is about 170 
grains, made up as follows : 

Aluminium rim ......... 76 grains. 

Eight needles ....... . . 54 ,, 

Aluminium nave ........ 2 ,, 

Aluminium and sapphire cap ... 2| ,, 

Paper ............. 28 

Silk thread ..... .... 8 , 


This is a seventeenth of the weight of the ordinary 
ten-inch compass hitherto in common use in the 
best-found merchant steamers, which is about 
six ounces. On the other hand, the vibrational 
period of the new ten-inch compass, which at 
Glasgow is about forty-two seconds, is nearly 
double that of the ordinary ten-inch compass. The 


frictional error of the new compass when tested 
in the most severe manner that is to say, by 
experiments on shore with the bowl resting on a 
perfectly steady support, first bringing a magnet 
near it so as to deflect the card several degrees, 
and then withdrawing the magnet so as to allow 
it to come back very slowly towards its true 
position of magnetic equilibrium is not more 
than a quarter of a degree. The whole magnetic 
moment of the eight needles of the new card is 
only about one-thirteenth of that of the two 
needles of an ordinary lo-inch card, and is so 
small that the error due to its inductive influence 
on the iron globes used for correcting the quad- 
rantal error is practically insensible, even in such 
extreme cases as when the quadrantal error 
corrected amounts to 10 or 15. The theoretical 
anticipation of advantage from the long vibra 
tional period in giving steadiness at sea, has 
been fully confirmed by three years' experience 
in iron sailing ships and steamers, some 
crossing the Atlantic, and others making voyages 
through the Mediterranean and round the Cape 


to India, China, and back by the West Indies, or 
to Australia and New Zealand. 

To produce steadiness of the compass-card in 
steamers which have powerful engines, and where 
there is much vibration, it has been customary 
to suspend the bowl by means of india-rubber 
bands. A serious objection to this method is that 
the india-rubber is liable to become rotten by ex- 
posure to heat or oil, especially if it is used in fine 
enough bands to give the requisite steadiness in all 
circumstances. After many trials of metallic springs 
in lieu of india-rubber, I at last found a plan of 
brass spring resembling a rope grummet, but with 
clastic brass wire instead of the rope strands, by 
which I succeeded in obtaining more satisfactory 
steadiness of the compass than with india- 
rubber. The construction of this brass grummet- 
ring and the mounting of the compass-bowl upon 
it, may be described as follows : A single wire is 
first bent and its ends are united by soldering 
or brazing, so as to form a ring of the proper size. 
This serves as a core on which a second brass 
wire is laid on spirally, six turns round the core. 


The ends of this second wire are also united by 
soldering or brazing, and thus an elastic ring is 
produced strong enough to support the compass- 
bowl. The compass-bowl is suspended from the 
elastic ring with the intervention of a rigid gimbal 
ring. The elastic ring has two sockets fixed at 
the ends of a diameter, which rests on two balls 
attached to the brass rim of the binnacle stand. 
The elasticity of the ring mitigates the effect on 
the knife-edges bearing the gimbal ring and bowl, 
and on the point bearing the compass-card, of 
vertical tremors of the platform on which the 
binnacle rests. The knife-edges of the gimbal 
ring are supported on two grooved stirrups, hung 
by chains from the elastic rings. This suspension 
mitigates the effect of horizontal tremors of the 

The most difficult and not the least interesting 
part of my subject remains, the deviation of the 
compass produced by magnetization of the ship 
herself, or of iron in her fittings or cargo, and 
practical appliances for relieving of these errors 
the compasses of iron ships ; but limits of space 


prevent me from more than very slightly touching 
on it in the present article. 

The magnetism of a ship's iron is a very 
variable property, and it is almost as difficult to 
classify and describe it in words as it is to correct 
its effect on the compass. It may be imagined 
to consist of two constituents : one permanent ; 
the other transient, because dependent on transient 
inductive influences. But the " permanent mag- 
netism " is not perfectly permanent, and therefore 
it is called " sub-permanent," or it is imagined 
as consisting of two parts, a thoroughly permanent 
part and a sub-permanent part. Then again, 
the " transient magnetism " is not perfectly tran- 
sient, but is sub-permanent. If the permanent 
magnetism were perfectly permanent, and the 
transient magnetism perfectly transient according 
to changes of the influence to which it is due, it 
would be easy to apply magnets and iron in the 
neighbourhood of the compass, so that, whatever 
might be the position of the ship, whether upright 
or heeling over, or in whatever part of the world 
she might be, the needle should point in exactly 


the same direction, and exhibit precisely the 
same return force when deflected from this direction, 
as it would were there no iron in the ship. It is 
only because of the approximate permanence of 
one part of the ship's magnetism, and the approxi- 
mate transience of the other, that the compass 
can be used at all in an iron ship as a guide for 
her course in the intervals between observations 
of sun, or moon, or stars. For the sake of simpli- 
city, and to avoid circumlocutions, I shall first 
describe the effects on the compass of the ship's 
magnetism, and explain how they are to be cor- 
rected on the supposition of perfect permanence 
and perfect transientness of its two constituents ; 
and afterwards shortly explain how the mariner 
must be constantly on his guard to determine 
and allow for unpredictable irregularities in his 
compass due to variations of the permanent mag- 
netism, and to retention of some of the transient 
magnetism when the inducing influence is past. 

The ship's permanent magnetism produces at 
the place of the compass a constant force in a 
direction which is constant relatively to the ship 



wherever she goes and however she turns. This 
force may be balanced by an equal and opposite 
force produced by a permanent magnet fixed in 
a proper position in the neighbourhood of the 
compass. Again, the transient magnetism induced 
in the ship's iron by the earth's magnetic force, 
however the ship may vary in position, whether 
by turning horizontally or heeling over in one 
place, or by going to different places on the earth's 
surface, may be balanced by an equal and opposite 
force due to magnetism induced in a properly- 
shaped mass of soft iron fixed in a proper posi- 
tion in the neighbourhood of the compass. 

Were our temporary supposition of perfect 
permanence and perfect transientness of the two 
constituents of the ship's magnetism rigorously 
correct, it would be quite practicable to thoroughly 
and accurately perform the whole adjustment. 
The measurements and calculations required to 
allow this to be done for any particular ship are 
only such as, in the process technically called 
" swinging the ship," and in the subsequent calcu- 
lation of the numbers A, B, C, D, E, in 


Archibald Smith's theory as set forth in the 
Admiralty Manual, are regularly performed at 
frequent intervals for every ship of the British 
Navy, with the addition that they would have to 
be performed not only for the ship upright, but 
also with a list of 10 or 15 to either side. If the 
supposition we have made for a moment as to per- 
fect definiteness of quality of the ship's magnetism 
were true, the whole of this process could be 
actually carried out in practice, and the labour 
required to move loads across the deck of the ship 
or shift cargo in the hold, so as to give her the 
requisite list to one side or other, would be well 
repaid by getting her compasses perfectly corrected 
once for all. But, alas ! the compass is not to be 
corrected perfectly once for all by any possible 
operations or observations, however accurately 
performed. The ship's permanent magnetism 
gradually changes, more or less rapidly according 
to circumstances, and readjustment becomes 
necessary ; sooner generally in a new ship, but 
sooner or later in every ship. The labour and 
expense of " swinging" the ship both upright and 

X 2 


with a list to either side, as it cannot give a perfect 
and permanent adjustment of the compass, is 
scarcely compensated by the approximate and 
merely temporary approach to perfection obtain- 
able by the complete process. Accordingly swing- 
ing the ship when heeled over is rarely performed 
in practice, but swinging on even keel is done 
regularly for every new ship, and at regular or 
irregular intervals, according to circumstances, for 
all iron ships in the course of their service. 

To " swing " a ship is a technical expression 
which means to turn her round with her head 
successively on all points of the compass, and de- 
termine the error of the compass for a sufficient 
number of different courses to allow it to be 
estimated with sufficient accuracy for every course. 
With plenty of sea room and with clear enough 
sky to see sun, moon, or stars, or with complete 
enough compass marks on land in view, the 
process is best performed under way. 

When the ship is to be swung, and it is not 
practicable or not convenient to do so under way, 
she must be taken to some place where there is 


little or no tidal current, and there anchored, and 
by aid of a tug or tugs, or by warps and anchors or 
fixed moorings and buoys laid out in proper 
positions, turned round all points of the compass 
and detained on each point on which the error is to 
be observed, or observed and corrected, long 
enough to allow the observation to be made and 
the requisite adjustment performed. 

A very simple method of taking advantage of 
this process not merely to determine the errors of 
the compass, but to annul them, which was worked 
out and published so long ago as 1837 by the 
Astronomer- Royal, Sir George Airy, has been in 
practical use, more or less, ever since. It consists 
in first placing steel magnets in proper positions 
within a few feet of the compass to correct the error 
on the north or south, and on the east or west 
courses, and then applying soft iron to correct a 
residual error, which is still found after the compass 
has been corrected on the cardinal courses. This 
residual error Airy called the quadrantal error, 
because it has its maximum value in either direc- 
tion when the ship's head is on one or other of 


the four quadrantal points, N.E., S.E., S.W. 
and N.W. The great lengths and the great mag- 
netic moments of the needles hitherto used in the 
marine compass rendered it practically impossible 
for the latter part of Sir George Airy's method to 
be carried out correctly in practice, except in cases 
in which the quadrantal error was much smaller 
than it generally is in modern iron ships. The 
primary object of my new form of compass de- 
scribed above, is to permit complete correction of 
the quadrantal error, not merely when its amount 
is from 5 to 7 or 8, which it generally is in iron 
sailing ships or steamers of ordinary modern types ; 
but even when it amounts to as much as 15 or 
20, as it is sometimes found to be in ironclads. 
A complete realization of Airy's method is thus 
now for the first time rendered practically possible 
for all classes of ships. The whole method essen- 
tially includes some plan for gradually changing 
the positions of the correcting magnets at sea to 
correct on the north, or south, or east, or west course 
when error is found to have sprung up, whether 
through change in the ship's sub-permanent mag- 


netism, or of the magnetism induced in her by 
the vertical component of the terrestrial magnetic 
force changing with her geographical position. 
The binnacle of my new compass contains 
appliances, for making, with ease and certainty, 
the proper changes in the adjustment of Airy's steel 
magnets, whenever observation shows change to be 
necessary. It has also an adjustable appliance for 
placing properly a steel magnet below the centre 
of the compass to correct the heeling error, accord- 
ing to a subordinate but still very important part 
of his complete method of correction. My 
binnacle has also appliances for placing and fixing 
once for all a pair of iron globes in proper 
positions on the two sides of the compass to cor- 
rect the quadrantal error. When the globes for 
correcting the quadrantal error have been once 
properly placed, no change of this adjustment is 
ever necessary for the same ship, and the same 
position of the compass in it, except in the case 
of some change in the ship's iron, or iron cargo, or 
ballast, sufficiently near the compass to sensibly 
alter the quadrantal error. But the magnetic cor- 


rectors for the semicircular error and the heeling 
error must be adjusted from time to time to keep 
the compass correct. 

Lastly it has an appliance for fixing on the for- 
ward or after side of the binnacle a bar of soft iron 
to realise conveniently a most important but long 
strangely neglected correction, 1 given so long ago as 
1 80 1 by Captain Flinders. This last appliance 
has been very successful in ships of the Peninsular 
and Oriental and Cape Mail Services. In the 
Union Steamship Company's ship Durban (Captain 
Warleigh), for instance, the first to which it was 
applied in connection with my compass, an error of 

1 Fifteen ships are reported by the Liverpool Compass Com- 
mittee as having had this correction applied to their steering com- 
passes with more or less complete success, but in every instance 
with decidedly good result. It was also applied with remarkable 
defmiteness and success to a compass in the ss. City of Mecca, 
by Captain Lecky, on a voyage between Bombay and the Clyde 
some years ago. An error of 14, found in the -English Channel 
on the east and west courses, after the compass had been perfectly 
corrected .by Airy's method a few weeks previously on the magnetic 
equator, was corrected by a vertical soft iron pillar, fixed to the 
ship in the neighbourhood of the compass. The result, proved in 
subsequent voyages of the ship, was most . satisfactory. I know no 
other cases in which the Flinders process had been used in iron ships 
before I commenced practising the process myself in 1878. 


34 degrees growing up in the voyage from England 
to Algoa Bay, and disappearing on her return to 
England, has been corrected by a Flinders bar 
attached to the front side of the binnacle, and the 
ship now goes and comes through that long voyage 
with no greater changes of compass error than 
might be experienced in the same time in a ship 
plying across the Irish Channel. 

The Flinders bar supplied with the compass is a 
round bar of soft iron, 3 inches in diameter, and of 
whatever length of from 6 inches to 24 inches is 
found to be proper for the actual position of the 
compass in any particular ship. To make up the 
proper length it is supplied in pieces of 12 inches, 
6 inches, 3 inches, i^ inches, and two pieces of f 
of an inch. In making up the proper length the 
longest piece should be uppermost and the others 
below it in order of their lengths. The weight of 
the bar is supported on a wooden column or bar 
resting on a pedestal fixed to the binnacle near its 
foot, this w r ooden bar being cut to such a length, or 
so made up of pieces, as to give the proper height 
to the upper end of the iron bar. The compound 


column of iron and wood is kept in position and 
protected from rain and spray by a brass tube 
with upper end closed, going down over it. 

The main object of the Flinders bar is to 
counterbalance the component of the ship's 
horizontal force on the compass, which is due to 
magnetism induced by the vertical component of 
the terrestrial magnetic force. Hence, in all 
ordinary cases, the ship's iron being symmetrical 
on the two sides of the fore-and-aft midship 
vertical plane, and the compass being placed in 
this plane, the Flinders bar must be placed in it 
also, and therefore must be exactly in the middle 
of the front side, or of the after side, of the 
binnacle. The Flinders bar essentially corrects, 
wholly and permanently, the constituent of the 
heeling error, which has its maximum values on 
the east and west courses. A subordinate object 
of the Flinders bar, as supplied to my compass, is 
to partially correct the constituent of the heeling 
error, which has equal maximum values on the 
north and south courses, by partially counter- 
balancing the component force on the compass, 


perpendicular to the ship's deck, exerted by that 
part of the ship's magnetism which is induced by 
the vertical component of the earth's magnetic 
force. For this object also the proper position of 
the bar is up and down in the middle of the 
forward or after side of the binnacle ; but for it the 
bar should be lowered a little below, or raised a 
little above, the position in which, without altering 
the length of the bar, it gives its maximum 
horizontal force on the compass. When it is not 
desired to make this contribution to the heeling 
correction by the Flinders bar, it should be placed 
with its top about 2 inches above the level of the 
needles of the compass-card. 

To understand the action of the Flinders bar 
suppose first the ship to be anywhere in the 
northern magnetic hemisphere. 1 The vertical 

1 The earth's surface is divided into two parts, called the north- 
ern and southern magnetic hemispheres, by a line called the magnetic 
equator, which is the line of no dip. This line is not a great circle 
like the true equator, but a sinuous line north of the true equator in 
all east longitude, and from 180 to 173 of west longitude ; and 
south of the equator in all west longitude less than 173. Its 
greatest distance on either side of the equator is where it cuts the 
coast of Brazil in about 17 south latitude. Its greatest distance 


force there is such as to pull the red end or pole 
of a magnetized needle downwards, and to repel 
the blue end upwards. It also has the effect of 
inducing magnetism in any mass of iron, so as to 
give it a transient magnetic quality marked with 
blue on the upper side or end and red on the lower 
side or end. Thus, in the northern magnetic 
hemisphere the Flinders bar is transiently mag- 
netized by the earth's vertical force in such manner 
that it acts like a great bar-magnet with its upper 
end blue and its lower end red. At the magnetic 
equator it loses its magnetism, and in the southern 
magnetic hemisphere it acquires magnetism in the 
opposite direction to that which it had in the 
northern hemisphere ; so that now its upper end is 
red and its lower end blue. As the ship moves 
from one hemisphere across the magnetic equator 
to the other, the magnetism of the Flinders bar 

north of the equator is in the Indian Ocean, which it crosses from 
Africa, a little south of Cape Guardafui, to the south of India, very 
nearly along the 10 parallel of north latitude and eastward across 
the mouth of the Bay of Bengal to the Malay Peninsula, still but 
little short of this degree of north latitude. A chart of lines of 
equal magnetic dip, such as the very convenient small scale one 
of the Admiralty Compass Manual, should be carefully studied. 


gradually 1 diminishes to zero, and then increases 
gradually in the contrary direction. The object to 
be attained in applying it to the binnacle is that 
with this gradual change of its magnetism, it shall 
always as exactly as possible counterbalance the 
changing part of the force on the compass, due to 
the part of the ship's magnetization which changes 
with the gradual change of the vertical component 
of the terrestrial magnetic force. If this changing 
part of the ship's disturbing force on the compass 
is a pull aft in the northern magnetic hemisphere, 
and a pull forward in the southern magnetic 
hemisphere, the Flinders bar must be on the 
forward side of the binnacle. On the other hand, 
if the regularly changing part of the ship's force be 
a pull forward in the northern hemisphere, and aft 
in the southern hemisphere, the Flinders bar must 
be on the after side of the binnacle. The former 
is the most frequent case for the chief navigating 
standard compass and for the steering compass of 

1 The change of polarity in vertical bars in the ship, which takes 
place in crossing the magnetic equator, has sometimes been falsely 
supposed to be abrupt, and mistakes in respect to compass courses 
have been made in consequence. 


modern mail steamers and merchant steamers 
generally, in which the steering and conning of the 
ship is done on a bridge forward of the engines, 
with considerably more than half of the ship behind 
it. It is also almost certain to be the case for an 
after steering compass, a few feet in advance of the 
top of the iron stern-post and rudder-head, in an 
iron steamer or sailing ship. The second above- 
mentioned case is what will generally be found for 
a compass anywhere in the after half of the ship's 
length, to within two or three yards of the stern- 
post. Most frequently it is not possible to ascertain 
which of the two is the actual case until the ship 
has made a voyage through regions presenting 
considerable differences of vertical magnetic force. 
Suppose now the first adjustment to have been 
made somewhere in the northern magnetic hemi- 
sphere, and suppose that as the ship goes to places 
of weaker vertical force, 1 the fore-and-aft correcting 

1 "Vertical force" is a short expression for the vertical com- 
ponent of the earth's magnetic force. It is reckoned as positive 
when the direction of its action upon a red pole is downwards, as in 
the northern hemisphere ; and negative when upwards, as in the 
southern hemisphere. At the magnetic equator it is zero. The 


force required to make the compass correct on the 
east or west points, is found to be less than at the 
beginning of the voyage. It is clear that part of 
the correction made by the magnets ought to have 
been made by the Flinders bar. But nothing need 
be done except to diminish the fore-and-aft pull 
by the magnets, as long as the ship is going to 
places of weaker vertical force. If without touching 
or crossing the magnetic equator the ship returns 
again to places of stronger vertical force, and if it 
is found that increased longitudinal pull is now 
required, this should be applied, not by the 
magnets, but by introducing a Flinders bar or by 
increasing the bar already in position. 

Generally, for a ship making passages to and fro 
through regions of considerably different vertical 

amount of the vertical force at any place is calculated by multiplying 
the value of the horizontal force given by the chart of lines of equal 
horizontal force of the Admiralty Manual by the tangent of the dip 
as given by the chart of lines of equal magnetic dip. Thus, for 
example, the tangent of the dip for the south of England being 2 '44, 
and the horizontal force there being called unity, the vertical force there 
is 2-44. The tangent of the dip at Aden is '09, and the horizontal 
force is 1*95 ; hence the vertical force there is '1755, or about T V of 
the vertical force at the south of England. 


force, whether she crosses the magnetic equator or 
not, the rule in respect of the fore-and-aft correction 
is as follows : 

Correct the deviations found by observation on the 
east or west courses by the fore-and-aft magnets when 
the ship is going to places of weaker, and by the 
Flinders bar when she is going to places of stronger, 
vertical force, wJiether in the southern or northern 

After a few voyages the proper proportion of 
correction by Flinders bar to correction by bar- 
magnets will be practically realized. 

For a ship with a compass permanently relieved 
of quadrantal error, and with a binnacle provided 
with these appliances for adjustment, the regular 
management of the compass at sea becomes very 
simple. Whenever an error exceeding two or three 
degrees is ascertained on any course, it may be 
corrected by a slight readjustment of the correcting 
magnets, performed in such a manner as not to 
disturb the direction which the needle would show 
if the ship were steered on a course at right angles 
to that on which the error is found. Occasionally, 


when the weather is favourable, a ship at sea should 
be steered for a few minutes three or four points 
first on one side and then on the other side of her 
proper course, and the compass corrected on each 
of the extreme courses by such a movement of the 
correcting magnets as shall not disturb its adjust- 
ment on the other. When this is done the compass 
will be correct on every course, provided always 
the ship remains on even keel. In the case of a 
steamer the detention involved by this process is 
always less than a quarter of the whole time which 
it occupies ; for, wnile steaming in a direction 42 
(or 3^ points) off her proper course, she is dimin- 
ishing the distance from her destination at three- 
quarters of the rate at which she diminishes it 
when on her course. Three minutes' detention by 
steering three or four points on each side of the 
course for ten minutes to correct the compass 
every day of suitable weather would be more than 
compensated by the security against compass errors 
thus afforded. But the detention will, in fact, 
generally be far more than made up by the 
straighter course which the ship will be enabled to 


steer ; and thus, even if importance is attached to 
the saving of minutes on the whole passage, this 
will be promoted by taking time to correct the 



^Being extract from United Service Institution Lecture, 

ABOUT thirty years ago, Sir Edward Sabine 
gave a method, in which, by aid of deflecting 
magnets properly placed on projecting arms at- 
tached to the prism circle of the Admiralty 
standard compass, a partial determination of the 
error of the compass could be performed at any 
time, whether at sea or in harbour, without the aid 
of sights of heavenly bodies or compass marks on 

1 A very complete account of the deflector in theory and practice 
is contained in a work by Captain Collet, of the French Navy, 
entitled, Traite Thtorique et Practique de la Regulation et de la 
Compensation des Com pas avec ou sans Rettvements (Challamel 
Aine, Paris), which has been translated into English by William 
Bottomley (Griffin, Portsmouth). 


shore. The adjustable magnetic deflector before 
you is designed for carrying out in practice 
Sabine's method more rapidly and more ac- 
curately, and for extending it, by aid of 
Archibald Smith's theory, to the complete de- 
termination of the compass error, y 
with the exception of the con- 
stant term " A" of the Admiralty 
notation, which in almost ever}* 
practical case is zero, and can 
only have a sensible value in 
virtue of some very marked 
want of symmetry of the iron- 
work in the neighbourhood of 
the compass. 1 When it exists 

1 I had a curious case lately of effect of 
unsymmetrical iron on a midship steering 
compass, due to a steam-launch about 30 
feet long placed fore-and-aft on the port 
side of the deck with its bow forward and 
its stern 5 or 6 feet before the thwart-ship 
line through the position of the compass 
(Fig. 41). The compass having been ad- 
justed by the globes and magnetic correctors 
to correct the quadrantal error (D), and the 
semi-circular error, it was found (as was 
expected) that the compass was correct on 
the east and west points, but showed equal 
westerly errors of about 3^ on the north 
and south points. There were, therefore, 
approximately equal negative values of 
"A" and "E" each i^. The captain 
was, of course, warned of the change he will find when he is 
relieved of the steam-launch at Rangoon, the port of his destina- 

V 2 


it can easily be determined once for all and 
allowed for as if it were an index error of the 
compass card, and it will, therefore, to avoid 
circumlocutions in the statements which follow, 
be either supposed to be zero or allowed for as 
index error. 

The new method is founded on the following 
four principles : 

(i.) If the directive force on the compass needles 
be constant on all courses of the ship, the compass 
is correct on all courses. 

(2.) If the directive force be equal on five 
different courses it will be equal on all courses. 

(3.) Supposing the compass to be so nearly 
correct or to have been so far approximately ad- 
justed, that there is not more than eight or ten 
degrees of error on any course, let the directive 
forces be measured on two opposite courses. If 
these forces are equal the compass is free from 
semicircular error on the two courses at right 
angles to those on which the forces were 
measured ; if they are unequal there is a semi- 
circular error on the courses at right angles to 

lion. The explanation of the westerly deviation when the ship's 
head was north or south, by the inductive magnetism of the steam- 
launch, according to which its stern would be a true north pole 
when the ship is on the north course, and a true south pole 
when the ship is on the south course, is obvious from the an- 
nexed diagram, in which the letters n, s, denote true north pole and 
true south pole of the induced magnetism in the steam-launch when 
the ship's head is north magnetic. 


those on which the forces were measured, amount- 
ing to the same fraction of the radian (57*3) that 
the difference of the measured forces is of their 

(4.) The difference of the sums of the directive 
forces on opposite courses in two lines at right 
angles to one another, divided by the sum of the 
four forces, is equal to the proportion which the 
quadrantal error, on the courses 45 from those on 
which the observations were made, bears to 57'3* 

The deflector may be used either under way or 
in swinging the ship at buoys. The whole process 
of correcting the compass by it is performed 
with the greatest ease and rapidity when under 
way with sea room enough to steer steadily on 
each course for a few minutes, and to turn rapidly 
from one course to another. For each operation 
the ship must be kept on one course for three or 
four minutes, if under way, by steering by aid of 
an auxiliary compass, otherwise by hawsers in the 
usual manner of swinging at buoys, or by means 
of steam-tugs. A variation of two or three 
degrees in the course during the operation will 
not make a third of a degree of error in the result 
as regards the final correction of the compass. 
The deflector reading is to be taken according to 
the detailed directions in sections 14 and 15 of the 
printed " Instructions." This reading may be 
taken direct on the small straight scale in the 
lower part of the instrument. The divided micro- 


meter circle at the top is scarcely needed, as it is 
easy to estimate the direct reading on the straight 
scale to a tenth of a division, which is far more 
than accurate enough for all practical purposes. 
This reading with a proper constant added gives, 
in each case, the number measuring in arbitrary 
units the magnitude of the direct force on the 
compass for the particular course of the ship on 
which the observation is made. 

The adjustment by aid of the deflector is quite 
as accurate as it can be by aid of compass marks 
or sights of sun or stars, though on a clear day at 
any time when the sun's altitude is less than 40, 
or on any clear night, the adjuster will of course 
take advantage of sights of sun or stars, whether 
he helps himself also with the deflector or not. 

The deflector consists of two pairs of small 
steel bar magnets attached to brass frames, jointed 
together and -supported on a sole-plate, which is 
placed on the glass cover of the compass-bowl 
when the ' instrument is in use. The two frames 
carry pivoted screw nuts, with right and left 
handed screws. A brass shaft, with right and left 
handed screws cut on its two halves, works in 
these nuts, so that when it is turned in either 
direction one of the two pairs of north poles is 
brought nearer to, or farther from, one of the two 
pairs of south poles, while the other two pairs of 
north and south poles are all in the line of the 
hinged joint between the two frames. This ar- 


rangement, which constitutes, as it were, a jointed 
horse-shoe magnet, adjustable to greater or less 
magnetic moment by increasing or diminishing 
the distance between its poles through the action 
of the screw, is so supported on its sole-plate that, 

FIG. 42. DD, the gimballed nuts ; CC, the right and left handed screws; a, a 
divided micrometer circle to aid when very minute measurement of the 
distance between the poles is wanted ; ABA'. ABA', the two frames jointed 
round an axis through BB of the first diagram, and perpendicular to the plane 
of the second diagram through its central point B ; NS, the effective true 
north poles and true south poles; HUH, the scale indicating the distance 
between them ; EG, the glass of the compass-bowl ; K, the foot resting in the 
central conical hollow ; L, one of the other feet ; F, the spring to keep pres- 
sure on the feet LL. When the screw is turned so as to bring DD nearer one 
another the distance between S and N is diminished, and the axis BB rises 
with its ends B, B, guided by two vertical slots, of which both are seen in 
plane in the first figure, and one in elevation in the second figure. 

when this is properly placed on the glass of the 
compass-bowl, the effective poles move to and fro 
horizontally about half an inch above the glass on 


the two sides of a vertical plane through its centre. 
The sole-plate rests on three feet, one of which, 
under the centre of gravity of the deflector, rests 
in the conical hollow in the centre of the glass. 
It is caused to press with a small part of its whole 
weight on the other two feet by a brass spring 
attached to the bottom of the sole-plate on the 
other side of the centre from these two feet, and 
pressing downwards on the glass. A brass pointer 
attached to the sole-plate marks the magnetic axis 
of the deflector. It projects from the centre, on 
the side of which is the pair of true north poles. 
Thus, if the deflector be properly placed on the 
glass of the compass-bowl, with the pointer over 
the north point of the card, it produces no deflec- 
tion, but augments the directive force on the needle. 
To make an observation, the deflector is turned 
round in either direction, and the north point of 
the card is seen to follow the pointer. The power 
of the deflector is adjusted by the screw, so that, 
when the pointer is over the east or west point of 
the card, the card rests balanced at some stated 
degree of deflection, which for the regular observa- 
tion on board ship is chosen at 85. A scale, 
measuring changes of distance between the 
effective poles of the deflector, is then read and 
recorded. For adjusting compass by aid of the 
deflector, the magnets are so placed that the 
deflector reading, found in the manner just 
described, shall be the same for the four cardinal 


courses ; and also for one of the quadrantal 
courses if the compass is sufficiently affected by 
unsym metrically placed iron to show any sensible 
amount of the " E" constituent of quadrantal error. 
When the deflector is to be used for determining 
the amount of an uncorrected error, according to 
principles (3) and (4) above, the magnetic value 
of its scale reading must be determined by 
experiment. This is very easily done on shore, 
by observations of its deflecting power when set by 
its screw to different degrees of its scale. 



\_Being extract from United Service Institution Lecture, 1878 ; 
with additions of date 1 890. ] 

AN important objection was made to me some 
years ago by Captain Evans against the use of 
quadrantal correctors in the Navy, that they would 
prevent the taking of bearings by the prismatic 
azimuth arrangement which forms part of the 
Admiralty standard compass. The azimuth mirror 
applied to the compass before you was designed 
to obviate that objection. Its use even for taking 
bearings of objects on the horizon is not interfered 
with by the globes constituting the quadrantal 


correctors, even if their highest points rise as high 
as five inches above the glass of the compass-bowl. 
The instrument may be described as follows : A 
tube, so placed that an observer looking down cen- 
trally through it sees the divisions on the compass- 
card beneath, is supported on a frame resting on the 

FIG. 43. 

cover of the bowl, and moveable round a vertical axis. 
In the tube is fixed a lens at such a distance from 
the compass-card that the degree divisions of its rim 
are in the principal focus. At the top of the tube 
a prismatic mirror is mounted on a horizontal 
axis, round which it can be turned into different 


positions when in use. In the two methods of 
observation which I am going to describe, the mirror 
covers about one half of the top of the tube ; the 
upper half in the first method and the lower half in 
the second. 

(i) When taking a bearing by the first method, 
the principle of which corresponds with the ordinary 
camera lucida, the observer turns the instrument 
round its vertical axis until the mirror and lens 
are fairly opposite to the object. He then looks 
through the lens at the degree divisions of the 
compass-card, and turns the mirror round its hori- 
zontal axis till he brings the image of the object to 
fall on the card. He then reads directly on the 
card the compass bearing of the object. Besides 
fulfilling the purpose for which it was originally 
designed, to allow bearings to be taken without 
impediment from the quadrantal correctors, the 
azimuth mirror has a great advantage in not 
requiring any adjustment of the instrument, such 
as that by which in the prism compass the hair 
is brought to exactly cover the object. The 
focal length of the lens is about 12 per cent, 
longer than the radius of the circle of the com- 
pass-card, and thus, by an elementary optical 
principle, it follows that two objects a degree 
asunder on the horizon will, by their images seen 
in the azimuth mirror, cover a space of ri2 of the 
divided circle of the compass-card seen through 
the lens. Hence, turning the azimuth instrument 


round its vertical axis through one degree will only 
alter the apparent bearing of an object on the 
horizon by "12. Thus it is not necessary to 
adjust it exactly to the direct position for the 
bearing of any particular object. If it be de- 
signedly put even as much as 4 awry on either side 
of the direct position, the error on the bearing 
would hardly amount to half a degree. If the 
instrument were to be used solely for taking 
bearings of the objects on the horizon, the focal 
length of the lens should be made exactly equal 
to the radius of the circle, and thus even the small 
error of '12 in the bearing for one degree of error 
in the setting would be avoided. But one of the 
most important uses of the azimuth instrument at 
sea is to correct the compass by bearings of sun or 
stars at altitudes of from o to 50 or 60 above the 
horizon. The actual focal length is chosen to suit 
an altitude of 27, or thereabouts, (this being the 
angle whose natural secant is ri2). Thus if two 
objects whose altitudes are 27, or thereabouts, and 
difference of azimuths i, are taken simultaneously 
in the azimuth mirror, their difference of bearings 
will be shown as one degree by the divided circle 
of the compass-card seen through the lens. Hence 
for taking the azimuth of star or sun at an altitude 
of 27, or thereabouts, no setting of the azimuth 
mirror by turning round the vertical axis is 
necessary, except just to bring the object into the 
field of view, when its bearing will immediately be 


seen accurately shown on the divided circle of the 
compass-card. This is a very valuable quality for 
use in rough weather at sea, or when there are 
flying clouds which just allow a glimpse of the 
object, whether sun or star, to be caught, without 
.allowing time to perform any adjustment, such as 
that needed in the old Admiralty azimuth compass 
to bring the hair, or rather the estimated middle 
of the space traversed by the hair in the rolling of 
the ship, to coincide with the object. The same 
degree of error as on the horizon, but in the 
opposite direction, is produced by imperfect ad- 
justment in taking the bearing of an object at an 
elevation of 38. 

Thus for objects from the horizon up to 38 of 
altitude the error in the bearing is less than 12 per 
cent, of the error of the setting. For objects at a 
higher elevation than 38 the error rapidly in- 
creases ; but even at 60 altitude the error on the 
bearing is a little less than half the error of the 
setting ; and it is always easy, if desired, to make 
the error of the setting less than a degree by 
turning the instrument so that the marker which 
you see below the lens, shall point within a degree 
of the position marked on the circle of the compass- 
card by the image of the object. 

For taking star azimuths the azimuth mirror 
has the great advantage over the prism compass, 
wit /i its then invisible hair, that the image of the 
object is thrown directly on the illuminated scale 


of the compass-card. The degree of illumination 
may be made less or more, according to faintness 
or brilliance of the object, by holding a binnacle 
lamp in the hand at a greater or less distance and 
letting its light shine on the portion of the 
compass-card circle seen through the lens. 
Indeed, with the azimuth mirror it is easier to 
take the bearing of a moderately bright star by 
night than of the sun by day ; the star is seen as 
a fine point on the degree division, or between 
two, and it is easy to read off its position instantly 
by estimation to the tenth of a degree. The 
easiest as well as the most accurate of all, 
however, is the sun when bright enough and high 
enough above the horizon to give a good 
shadow on the compass-card. For this purpose 
is the stout shadow-pin which you see mounted 
on the framework of the azimuth mirror per- 
pendicularly to the glass and through the central 
bearing point of the compass. 

(2) Bearings can also be taken with this instru- 
ment by looking direct at the object over the top 
of the prism which is the second method referred to 
above. The degrees of the card reflected in the 
prism are then seen close below the object. This 
method is applicable to objects on the horizon, 
and is more particularly useful for taking bearings 
of distant landmarks which are too indistinct to 
be seen when reflected in the prism. 

For taking bearings by this method the prism 


is kept turned (arrow-head down) with its 
mounting-stopper against the framework. The 
observer turns the instrument round its vertical 
axis till the prism and lens are fairly opposite to 
the object, then places his eye so as to see the 
object over the prism and reads the bearing of 
the object from the compass-card as seen re- 
flected in the prism. 

The pointer is used merely as an aid in 
directing the instrument towards the object, but 
the bearing is read directly from the object as seen 
on the compass card. It is not necessary that 
the pointer should be pointing exactly towards 
the object unless the altitude be very high. For 
objects from horizon up to 38 of altitude the error 
on the bearing, as in the first described method, 
would be less than half a degree, even if the pointer 
were pointing 4 away from the object. 

Another advantage of the azimuth mirror 
particularly important for taking bearings at sea 
when there is much motion, is that with it it is 
not necessary to look through a small aper- 
ture in an instrument moving with the compass- 
bowl, as in the ordinary prism compass, or in the 
original nautical azimuth compass (described 280 
years ago by Gilbert, Physician in Ordinary to 
Queen Elizabeth, in his great Latin book, On 
tJie Magnet and on the Rarth a great Magnet], 
which is very much the same as that still in use 
in many of the best merchant steamers. In using 


the azimuth mirror the eye may be placed at any 
distance, of from an inch or two to two or three 
feet, from the compass, according to convenience, 
and in any position, and may be moved about 
freely through a considerable range on either side 
of the line of direct vision through the lens, 
without at all disturbing the accuracy of the 
observation. This last condition is secured by 
the lens being fixed in such a position of the 
instrument that the divided circle of the compass- 
card is in its principal focus. Thus the virtual 
image of the divided circle is at an infinite 
distance, and the images of distant objects seen 
coincidently with it by reflection in the plane 
mirror show no shifting on it, that is to say, no 
parallax, when the eye is moved from the central 
line to either side. From the geometrical and 
optical principles explained previously, it follows 
also that if the azimuth instrument be used for 
taking the bearing of an object whose altitude 
exceeds 27, then the effect of turning the frame 
carrying the lens and mirror in either direction 
will seem to carry the object in the same direction 
relatively to the degrees of the card ; or in the 
contrary direction if the altitude is less than 27. 
But if the altitude of the object be just 27, then 
the azimuth instrument may be turned through 
many degrees on either- side of the compass -card, 
without sensibly altering the apparent positions of 
the objects on the degree-divisions. 


\JPaper communicated to the Society of Telegraph Engineers, 
April 22nd, 1874] 

ON the 29th of June, 1872, I sounded, from the 
Lalla Rookh scliooner-yacht, in the Bay of 
Biscay, with a lead weight of 30 Ibs., hung by 19 
fathoms of cod-line from another lead weight 
of 4 Ibs. attached to one end of a three-mile coil 
made up of lengths of pianoforte wire spliced 
together, and wound on a light wheel about a 
fathom in circumference, made of tinned iron plate. 
The weight was allowed to run directly from the 
sounding-wheel into the sea, and a resistance 
exceeding the weight in water of the length of the 
wire actually submerged at each instant was applied 
tangentially to the circumference of the wheel, by 

VOL. in. z 


the friction of a cord wound round a groove in the 
circumference, and kept suitably tightened by a 
weight. My position at the time was considerably 
nearer the north coast of Spain than a point where 
the chart shows a depth of 2,600 fathoms, the 
greatest depth previously marked on the charts of the 
Bay of Biscay. When from 2,000 fathoms to 2,500 
fathoms were running off the wheel, I began to have 
some misgivings as to the accuracy of my estima- 
tions of weights and application of resistance to the 
sounding-wheel. But, after a minute or two more, 
during which I was feeling more and more anxious, 
the wheel suddenly stopped revolving as I had ex- 
pected it to do a good deal sooner. The impression 
on the men engaged was that something had broken ; 
and nobody on board except myself had, I believe, 
the slightest faith that the bottom had been reached. 
The wire was then hauled up by four or five men 
pulling on an endless rope round a groove on one 
side of the wheel's circumference. After about 1 ,000 
fathoms of wire had been got in, the wheel began 
to show signs of distress. I then perceived, for the 
first time (and I felt much ashamed that I had not 


perceived it sooner), that every turn of wire under 
a pull of 50 Ibs. must press the wheel on the two 
sides of any diameter with opposing forces of 
IOO Ibs., and that therefore 2,240 turns, with an 
average pull on the wire of 50 Ibs., must press the 
wheel together with a force of 100 tons, or. else 
something must give way. In fact the wheel did 
give way, and its yielding went on to such an extent 
that when 500 fathoms of wire were still out the 
endless cord which had been used for hauling 
would no longer work on its groove. The remain- 
ing 500 fathoms and the 30 Ibs. sinker were got in 
with great difficulty by one man working at a time 
in an awkward position over the vessel's side, 
turning the wheel slowly round by a handle. I was 
in the greatest anxiety, expecting at any moment 
to see the wheel get so badly out of shape that it 
would be impossible to carry it round in its frame, 
and I half expected to see it collapse altogether 
and cause a break of the wire. Neither accident 
happened, and, to our great relief, the end of the 
wire came above water, when instantly the 19 
fathoms of cod-line were taken in hand and the 

Z 2 


30 lb. sinker hauled on board. I scarcely think any 
one but myself believed the bottom had been 
reached until the brass tube with valve was un- 
screwed from the sinker and showed an abundant 
specimen of soft grey ooze. The length of wire and 
cod-line which had been paid out was within a few 
fathoms of being exactly 2,700 fathoms. The wire 
was so nearly vertical that the whole length of line 
out cannot have exceeded the true depth by more 
than a few fathoms. The position was accurately 
determined by two Sumner lines observed at nh. 
23m. a.m. and ih. 5m. p.m. Greenwich apparent 
time, and found by their intersection to be latitude 
44 32', longitude 5 43' west. 

That one trial was quite enough to show that the 
difficulties which had seemed to make the idea of 
sounding by wire a mere impracticable piece of 
theory have been altogether got over. 

The great merit of wire compared with rope is the 
smallness of the area and the smoothness of the 
surface which the wire presents, in contrast with 
the greatness of the surface and its roughness, when 
rope with a comparable degree of strength is used. 


The wire that I have found suitable is pianoforte 
wire of the Birmingham gauge No. 22. It w r eighs 
about 14 J Ibs. to one nautical mile, and bears from 
230 Ibs. to 240 Ibs. without breaking. The quality 
of wire which I described to the meeting of the 
British Association at Brighton was special wire 
made for the purpose by Messrs. Johnson, the 
celebrated wire-makers of Manchester. They suc- 
ceeded in producing a length of crucible steel wire 
of three miles in one piece, which certainly was a 
great feat in the w r ay of wire-making. This wire 
was supplied by them to me as capable of bearing 
a pull of about 230 Ibs. I tested many specimens 
of it, and I found that none of them broke with a 
less pull than about 220 Ibs., and many of them 
bore as much as 240 Ibs. The wire then fulfilled 
all that the makers promised, and it had that 
quality which then seemed of paramount importance 
a great length in one piece of metal. The truth 
is, that one of the supposed " impossibilities " was 
safe splices. However, splices must be made : and 
in my first trials I succeeded by making a long 
twist of two pieces of wire together, and running 


solder all along the interstices. On testing this 
splice, I found that, although it would bear within 
10 Ibs. or 20 Ibs. of the full breaking- weight of the 
wire, yet in every case the wire broke at the 
splice. This was precisely in accordance with 
theory. The sudden change of area of section 
between the long cylindrical wire, and the thicken- 
ing produced by the solder, is an essential element 
of weakness, of a character well known to engineers. 
Inevitably, if the wire is of uniform character, it 
breaks close beside the solder. To avoid this 
weakening of the wire, an exceedingly gradual 
commencement of the force by which one piece of 
wire pulls the other must be attained. The obvious 
way of attaining this is by a very long splice. A 
splice of two feet long I have found quite sufficient ; 
but three feet may be safer. The two pieces of 
wire to be spliced are first prepared by warming 
them slightly and melting on a coating of marine 
glue to promote surface friction. About three feet 
of the ends so prepared are laid together and held 
between finger and thumb at the middle of the 
portions thus overlapping. Then the free foot and 


a-half of wire on one side is bent close along the 
other in a long spiral, with a lay of about one turn 
per inch, and the same is done for the free foot and 
a-half on the other side. The ends are then served 
round firmly with twine, and the splice is complete. 
I have tested scores of splices made in this way, 
and in no one instance, even with splices only one 
foot long, did the wire break in the splice or near to 
it. It always broke some distance away, showing 
that the wire close to the splice was as strong as other 
parts of the wire, and of course in the splice itselt 
the two wires together give a greater strength 
than exists anywhere else. In upwards of one 
hundred soundings on the East and North coasts 
of Brazil, and in the Bay of Biscay, in depths of 
from 500 to 2,700 fathoms, partly with Johnson's 
special wire, and partly with Webster and 
Horsfall's, there has in no one instance been a 
failure of the splice. The splice is made very 
easily, and in a few minutes. 

The difficulty with regard to splices being 
altogether got over, we are freer in our choice 
of the wire to be used. Mr. Johnson tells me that 


it is impossible to produce in the great lengths the 
same quality of wire as is habitually made by the 
best makers of pianoforte wire. He said that, 
although he could produce wire of great strength, 
he found it impossible to attain the same temper 
as that of the pianoforte wire. Acting upon his 
valuable advice, I have now begun to use piano- 
forte wire of the best quality. Wire of an 
inferior quality is brittle at places, and breaks 
when it kinks. I believe not a single case of 
this has happened with the Webster and 
Horsfall pianoforte wire now used. 

The lengths which Webster and Horsfall 
supply of this wire are about 200 yards. But 
a splice in every hundred fathoms is no 
inconvenience whatever. Perhaps it is rather 
an advantage : because, practically the vigilance 
required to prevent accident through the 
stripping of a splice by any sharp obstacle 
is apt to flag dangerously if the passage of a 
splice is a rare occurrence. 

The most serious defect of the simple 
apparatus which I used in my first deep-sea 


sounding in the Bay of Biscay was the destruc- 
tive stress experienced by the wheel in haul- 
ing in the wire. 

My first attempt to remedy this defect was 
a failure. It consisted in stopping the hauling 
every twenty turns, taking the strain off the wire 
by aid of a clamp, and easing it round the wheel. 
This was done in a sounding of 1,200 fathoms, 
made in Funchal Bay, Madeira, only a few 
miles from Funchal, during the Hooper cable 
expedition to Brazil last summer. I found 
that stopping every twenty turns did not seem 
to be of any use at all, so I stopped every 
ten turns, and even that tedious process did 
not afford sufficient relief. That plan having 
proved a failure, I then looked out for some 
other ; and the peculiarity of the apparatus 
now before you consists in the way in which 
the difficulty was overcome. In the American 
Navy another mode of getting over it has 
been followed : the wheel has been strengthened, 
and a trigger apparatus has been introduced 
for detaching the weight when it reaches the 


bottom. This of course very much lightens the 
pull in hauling in the wire. By those means the 
strengthening of the wheel and the lightening of 
the pull the Americans got over the difficulty 
very well. I, however, did not consider it desir- 
able to throw away 30 Ibs. or 35lbs. of lead at every 
sounding, as I believed I could modify the appara- 
tus so as to make it easy to bring up the sinker 
from any depth not exceeding 3,000 or 3,500 
fathoms in ordinarily favourable circumstances ; 
and I wished to reserve the expedient of de- 
taching the weight for greater depths or less 
favourable circumstances. In case of very 
great depths. 4,000 fathoms or more, it will 
probably be desirable to use a heavier sinker, 
say 100 Ibs., and a trigger apparatus for 
detaching it when it reaches the bottom. But 
for depths not exceeding 3,000 fathoms, I 
prefer generally a 30 Ib. or 35 Ib. sinker, with 
no detaching apparatus. 

The way in which I have got over the diffi- 
culty of saving the main sounding wheel from 
destruction or damage by the pressure of the 


wire coiled on it, under heavy pull, consists 
in the use of an auxiliary hauling-in pulley by 
which the pull on the wire is very much 
reduced before it is coiled on the main 
sounding wheel. As in my original process 
in the Bay of Biscay, during the descent of 
the sinker the wire runs direct down into the 
sea from the main sounding wheel, which, for 
that part of the process, is placed in an over- 
hanging position on either side of the ship, or 
over her taffrail ; the taffrail, suppose, to avoid 
circumlocutions. To prepare for hauling in, a 
spun yarn stopper, attached to the lower fram- 
ing of the sounding machine projecting over 
the taffrail, or to the taffrail itself, is applied 
to the wire hanging down below, to hold the 
wire up and relieve the wheel from the necessity 
of performing that duty : or otherwise, two men, 
with thick leather gloves, can easily hold the 
wire up. A little of the wire is then paid out 
from the wheel ; the wheel with its framing 
is run inboard about five feet on slides which 
carry its framing ; and the slack wire is led 


over a quarter circumference of a "castor- 
pulley," mounted on the ship's taffrail, and three- 
quarters, or once and three-quarters, round an 
" auxiliary pulley " inboard. This pulley over- 
hangs the bearings of its own axle, so as to 
allow the loop or the two loops of the wire to 
be laid on it. Two handles attached to the shaft 
)f the auxiliary pulley, worked by one man on 
^ach or two men on each, take from two-thirds 
to nine-tenths of the strain off the wire before 
it reaches the main sounding wheel, on which 
it is coiled by one man or two men working on 
handles attached to its shaft. 

If the ship is hove to when the wire is 
being hauled in over the castor-pulley on the 
taffrail, the wire will generally stream to one side. 
By having the bearing of the stern pulley, an 
oblique fork turning round a horizontal axis (like 
the castor of a piece of furniture laid on its 
side), the wire is hauled in with ease though 
streaming to either side, at any angle. 1 This 

1 An improvement was made on the first arrangement of 
framing for bearing the castor axle of the forked piece in which 


castor arrangement is a very important addition 
to the hauling-in gear. By means of it it is 
easy to keep the wire on the stern pulley when 
the ship is rolling very heavily. Even on the 
steam launch of the Hooper, rolling sharply 
through great angles off Funchal Bay, a small 
castor pulley which I used accommodated itself 
perfectly to the motion, and allowed the wire 
to be coiled safely on the sounding wheel, 
which would have been scarcely possible without 
the aid of some such appliance. The quick- 
ness with which the wire allows the sinker to 
descend, and the ease of getting it on board 
again by aid of the castor pulley, notwithstand- 
ing a considerable degree of lateral drifting of 
the ship, render it easy to take deep-sea 
soundings of 2,000 or 3 ; ooo fathoms, from a 
sailing vessel hove to in moderate weather. 

But it is not necessary to keep the ship 
hove to during the whole time of hauling in 

the castor wheel or pulley runs, which consisted merely in 
lengthening the castor axle, and providing for it two bearings, 
instead of its having only one, as was the case in the machine 
shown at the meeting. 


FIG. 44. Apparatus for Deep-Sea 


the wire. When the depth exceeds 3,000 
fathoms, it will, no doubt, be generally found 
convenient to keep the ship hove to until a 
fe\v hundred fathoms of the wire have been 
brought on board. When the length out does 
not exceed 2,500 fathoms, the ship may be 
driven ahead slowly, with gradually increasing 
speed. When the length of wire out does not 
exceed 1,500 fathoms, the ship may be safely 

driven ahead at 
five or six knots. 
The last 500 fa- 
thoms may be got 
on board, with 
ease and safety, 
though the ship is 
going ahead at ten 
or twelve knots. 
Thus, by the use 
of wire, a great 
saving of time is 
effected ; for in the 


ordinary process the hemp rope must be kept as 


nearly as possible up and down, until the whole 
length out does not exceed a few hundred fathoms. 

[Sir William Thomson next proceeded to 
explain in detail and to exhibit in action a 
new sounding machine which had been made 
according to his designs by Mr. White of Glas- 
gow for Messrs. Siemens, to be used on board 
their cable ship Faraday, and which, through 
their kindness, was exhibited before the Society.] 1 

The wire is coiled on a large wheel (of 
very thin sheet iron galvanised), which is 
made as light as possible, so that when the 
weight reaches the bottom the inertia of the 
wheel may not shoot the wire out so far as 
to let it coil on the bottom. The avoidance 
of such coiling of the wire on the bottom is 
the chief condition requisite to provide against 
the possibility of kinks ; and for this reason 
a short piece of hemp line, about five fathoms 
in length, is interposed between the wire and 

1 The accompanying drawing (Fig. 44) shows the whole appara- 
tus with the sounding wheel in its inboard position for hauling in 
the wire. Detailed drawings are published in the Proceedings of 
the Philosophical Society of Glasgow for Session 1873-4. 


the sounding weight ; so that, although a 
little of the hemp line may coil on the 
bottom, the wire may be quite prevented 
from reaching the bottom. A galvanised 
iron ring, of about half a pound weight, 
is attached to the lower end of the wire, 
so as to form the coupling or junction 
between the wire and the hemp line, and to 
keep the wire tight when the lead is on the 
bottom, and the hemp line is slackened. The 
art of deep-sea sounding is to put such a 
resistance on the wheel as shall secure that 
the moment the weight reaches the bottom 
the wheel will stop. By " the moment " I 
mean within one second of time. Lightness 
of the wheel is necessary for this. The 
circumference of the wheel is a fathom, with 
a slight correction for the increased diameter 
from the quantity of wire on. Whatever 
length of wire is estimated as necessary to 
reach the bottom is coiled on the wheel. 
For a series of deep-sea soundings, in depths 
exceeding 1,000 fathoms, it is convenient to keep 


a length of 3,000 fathoms (about 43 Ibs.) coiled 
on the wheel. When we do not get bottom 
with 3,000 fathoms, the process of splicing on a 
new length of wire ready coiled on a second 
wheel, is done in a very short time two 
minutes at most. The friction brake which 
you see is simpler in construction than that 
shown to the Institution of Engineers in 
Scotland last session, and sent out a year 
ago to the American Navy Department The 
brake on the sounding machine now before 
you is a return to the simple form of brake 
which I used in June, 1872, when I first 
made a deep-sea sounding with pianoforte wire 
in the Bay of Biscay, in 2,700 fathoms. 

A measured resistance is applied systema- 
tically to the wheel, always more than enough 
to balance the weight of the wire out. The 
only failures in deep-sea soundings with 
pianoforte wire hitherto made have been 
owing to neglect of this essential condition. 
The rule I have adopted in practice is to 
apply resistance always exceeding by 10 Ibs. 


the weight of the wire out. Then, the sinker 
being 34 Ibs., we have 24 Ibs. weight left for 
the moving force. That, I have found, is 
amply sufficient to give a very rapid descent 
a descent so rapid that in the course of half 
an hour, or three-quarters of an hour, the bottom 
will be reached at a depth of 2,000 or 3,000 
fathoms. The person in charge watches a 
counter, and for every 250 fathoms (that is 
every 250 turns of the wheel) he adds such 
weight to the brake-cord as shall add 3 Ibs. 
to the force with which the sounding-wheel 
resists the egress of the wire. That makes 
1 2 Ibs. added to the brake-resistance for every 
1,000 fathoms of wire run out. The weight 
of 1,000 fathoms of the wire in the air is 
i4Mbs. In water, therefore, the weight is 
about 1 2 Ibs. ; so that if the weight is added 
at the rate I have indicated the rule stated 
will be fulfilled. So it is arranged that when 
the 34 Ibs. weight reaches the bottom, instead 
of there being a pull or a moving force, of 
24 Ibs. on the wire tending to draw it through 

A A 2 


the water, there will suddenly come to be a 
resistance of lolbs. against its motion. A 
slight running on of the wheel one turn at 
the most and the motion is stopped. The 
instantaneous perception of the bottom, even 
at so great a depth as 4,000 fathoms, when 
this rule is followed is very remarkable, and 
has been particularly noticed by Commander 
Belknap in reports of his soundings in the 
Pacific, presented to the United States Navy 

As to the modes of accelerating the 
process : first, when there are plenty of men 
available, instead of handles I put on each 
end of the shaft of the auxiliary hauling-in 
pulley, a smaller pulley with a sharp V- 
groove. An endless rope passed half round 
each of these V-pulleys, and kept tight by a 
snatch block suitably placed inboard, allows 
any number of men to haul, hand over hand, 
or walking along the deck, as may be found 
most convenient. Or when there is a donkey- 
engine, it may be employed on one of the 


endless ropes instead of a multitude of men 
on the two. By multiplying the speed of 
men, or using a donkey-engine in that way, 
there is no difficulty in hauling in the wire 
at the rate of about eight nautical miles an 
hour. Thus the last 1,000 fathoms of wire, 
with 34 Ibs. sinker attached, may in any case 
be easily and safely got on board in seven 
or eight minutes ; but a dozen men hauling 
together might be required for this speed. 
When greater lengths of wire are out, slower 
speeds of hauliiig are required for safety. 
With 3,000 fathoms of wire out, probably an 
average speed of four miles per hour (or 400 
feet per minute) would not give more than 
from 100 to 120 Ibs. whole pull on the in- 
coming part of the wire (or from 30 to 
50 Ibs. resistance of the water, added to 
34 Ibs. weight of sinker and 36 Ibs. weight in 
water of the wire) ; and would, therefore, be 
a safe enough speed. Of course, if there is 
a heavy sea, augmenting considerably the 
maximum stress above the mean stress, then 


slower hauling must be practised. An arrange- 
ment by Professor Jenkin can very readily 
be applied, by which the men or engine can 
haul in as fast as they please, and be unable 
to put more than a certain force on the 
wire. Thus will be realised in speed the 
benefit of abundance of power. The wire 
will come in fast when the strain is easy, 
and not come in at all when the ship is 
rising and producing such a pull on the wire 
as might break it if being hauled in at the 

The advantages of the pianoforte-wire method 
are very obvious. You see the simplicity of 
the apparatus, and the comparative inexpen- 
siveness of it ; no donkey-engine required, no 
three or four hundred pounds of iron cast 
away every time, as in the ordinary method 
of deep-sea soundings : and withal there is a 
very much surer sounding than the ordinary 
process can give at the same depths. The 
apparatus at present in use in our navy, 
which is better than that of any other navy 


in the world at this moment, except the 
American, is, as I know by actual experience 
of it, more difficult and tedious, and less 
sure at 500 fathoms, than sounding by the 
pianoforte wire at 2,000 fathoms. And lastly, 
there is the possibility of effecting a sounding 
in cases in which, as in the case of the 
Challenger in the Gulf Stream, the most 
matured previous process fails altogether. I 
think it highly desirable that the new method 
should be taken up by our own Admiralty. 
But innovation is very distasteful to sailors. 
I have a semi-official letter to the effect 
" When you have your apparatus perfected we 
may be willing to try it." I may say that 
it seems a little strange that after my having 
intimated, in the month of July 1872, the 
perfect success of pianoforte wire for sounding 
in depths of 2,700 fathoms, the Challenger 
was allowed to go to sea without taking 
advantage of this process, and that a year 
and a half later I should be told "When 
you have perfected your instrument we may 


give it a trial." The American Navy depart- 
ment looked upon the matter with different 
eyes, and certainly treated my proposal in a 
very different spirit. They found my ap- 
paratus full of defects. They never asked me 
to perfect it, but they perfected it in their 
own way, and obtained excellent results. I 
went on independently in another line, and made 
a considerably different apparatus from that 
which is now being used by the Americans ; 
but I certainly was very much struck by the 
greal zeal and the great ability which the 
American naval officers showed in taking up 
a thing of this description, which had merely 
been proved to be good, and charged them- 
selves with improving the details and making 
it a workable process. 

If I may be allowed two or three minutes 
longer, I will describe the method of making 
flying-soundings with wire. In the first Hooper 
expedition, to lay the first section of the 
Western and Brazilian Company's cable from 
Pernambuco to Para, the Brazilian Govern- 


ment sent the gun-boat Paraense with us to 
take soundings, but the coal would not carry 
her the whole way, and over the remainder 
of it we were left to our own resources for 
soundings. Wire soundings had been taken 
over the route previously by Mr. Galloway, 
in a steamer chartered for the purpose by 
the Western and Brazilian Telegraph Company, 
and again in the Paraense^ so as to give a 
general idea of the line to be taken for the 
cable ; but still it was very important that 
soundings should be taken during the actual 
laying. Accordingly, Captain Edington arranged 
that my sounding-wheel should be set up over 
the stern of the Hooper, and soundings were taken 
every two hours, without stopping the ship. 
A 30 Ibs. weight was hung by a couple of 
fathoms of cord from the ring at the end of 
the wire. Then the wheel was simply let go, 
with a resistance of about 6 Ibs. on its cir- 
cumference, the ship running at the rate of 
4^ knots, relatively to the surface-water (or at 
6 knots relatively to the bottom) ; and after, 


perhaps, 150 fathoms had run out in some 
cases 175 fathoms suddenly the wheel would 
almost stop revolving. In half a turn it was 
obvious that there was this sudden difference 
which showed that the sinker had reached the 
bottom. The moment the difference was 
perceived, the man standing by laid hold 
of the rim of the wheel and stopped it. 
Thus we achieved flying-soundings in depths 
of 150 fathoms, with the ship going through 
the water at the rate of 4^ knots, and 
obtained information of the greatest possible 
value with reference to the depth of the 
water and the course to be followed by the 
cable. I think this is of such great import- 
ance that I never would like to go to lay a cable 
without an apparatus for flying-soundings. The 
warning that this practice gives of shallow 
water, or of too great a depth of water, has 
a value which the members of the Society of 
Telegraph Engineers will readily appreciate. 
It will also, no doubt, be found useful in 
ordinary navigation. There is one interesting 


topic to which I may refer, in conclusion, 
and that is the sound continually produced 
by the wire. All the time we are employing 
pianoforte wire in this way we have " sounding " 
in a double sense. During the whole process 
of sounding we are continually reminded of 
the original purpose of pianoforte wire by the 
sounds it gives out. A person of a musical 
ear can tell within a few pounds what pull 
is on the wire by the note it sounds in the 
length between the castor-pulley at the stern 
and the haul-in drum which is about five 
feet inboard of it. 

There are two methods of guarding against rust 
of the wire. The Americans used oil submerging 
the wheel in oil when it was out of use. Com- 
mander Belknap having carried out the process of 
wire-sounding with remarkable success, I suppose 
that the Americans are satisfied with the pre- 
serving power of the oil thus used. On board 
the Hooper the deep-sea sounding-wire was pre- 
served by caustic soda when out of use. That 
substance, when bought wholesale, was so inex- 


pensive that the cost of that mode of keeping 
the wire from corrosion was not worth speaking of. 
There is, however, a good deal of trouble con- 
nected with it ; but it must be remembered that 
that trouble would not be much regarded on 
board a ship appointed especially for making 
soundings. The preserving effect of alkali upon 
steel is well known to chemists. It seems to be 
due to the alkali neutralising the carbonic acid in 
water, for the presence of carbonic acid in water is 
the great cause of iron being corroded. The fact 
is well established that iron would remain perfectly 
bright in sea-water rendered alkaline by a little 
quick-lime. Caustic soda is a more sure material, 
because with it we can make more certain that the 
water is really alkaline. I am told by a very 
excellent authority Mr. James Young, that, 
whether caustic soda or quick-lime is used, all 
that is necessary, in order to make sure that the 
pickle will be a thorough preserver of the wire is 
that it should be found to be alkaline when tested 
with the ordinary litmus test-paper. The American 
experience is, that although the caustic soda 


preserved the wire, it eats away the solder, and on 
that account they prefer to use oil. 

[Sir. W. Thomson in reply to questions that had 
been put said] : I have been asked to explain how 
the resistance is applied on this apparatus. I will 
state in the first place that this form of brake was 
patented by me in 1858. and I have used it myself 
ever since. 

[Demonstrating the use of the brake, Sir W. 
Thomson remarked] : The rate of change of pull in 
the cord per radian 1 round the wheel is equal to 
the amount of the pull at any point, multiplied by 
the coefficient of friction. The whole tangential 
resistance which the cord applies to the circum- 
ference of the wheel is equal to the excess of pull 
at one end above that at the other end of the cord. 
I have been asked by Mr. Latimer Clark whether I 
recover the sinker in flying soundings. Always : I 
never lose a pound of lead if I can help it. In the 
use of the " deep-sea lead " of ordinary navigation, 

1 " Radian " is a most valuable word, introduced by Professor 
James Thomson to denote the angle whose arc is equal to radius. 
It is the hitherto nameless "unit angle" of the Cambridge and other 
mathematical books. 


six men have a heavy haul to bring up a lead in 
soundings of 50 or 60 fathoms, if the ship is under 
way ; but by the wire process a cabin boy can 
bring a 34 Ibs. sinker with ease from a depth of 150 
fathoms the ship all the time going on her course, 
at from four or five knots (to which the speed may 
have been reduced for a couple of minutes for the 
sounding) up to full speed. 

An important merit of wire for deep-sea sounding 
is the setting of the ship in motion again, which it 
permits almost as soon as the bottom is reached. 
Suppose the depth found 3,000 fathoms, by the 
time you have got about 500 fathoms of wire in, 
you steam slightly ahead ; when 1,500 fathoms is 
in, you may steam at five or six knots without 
injury ; and by the time you have only about 1,000 
fathoms out, you may steam at 10 knots ; and, if 
the speed of the ship is equal to it, you may steam 
at 12 knots with 700 or 800 fathoms of line out. 
In fact, the time spent in deep-sea soundings will 
be reduced to a small fraction of what it is by the 
process of our own Admiralty. Mr. Siemens has 
asked, how quickly a sounding of 2,000 fathoms can 


be made. The wire, with 34 Ibs. sinker, would take 
not more than 30 minutes to run out ; but, if for a 
tour deforce you wished to do it quicker than that, 
I should use a much greater weight, say 150 Ibs., 
with detaching trigger. Supposing, however, the 
34 Ibs. sinker to be used, with the multiplying 
speed on the pulleys, and twelve or fourteen men 
hauling on the endless rope, it might be hauled 
from a depth of two miles in about 15 minutes. 
Thus the whole process, with the recovery of the 
sinker, would be performed in 45 minutes. The 
process without recovery of the 150 Ibs. sinker may 
be made with only about twenty minutes' detention, 
when the object is to make a sounding with the 
least possible detention, and, therefore, the ship is 
allowed to go on her course at fair speed during the 
time of hauling in the line, with tube and specimen 
of bottom. A sounding of 1,000 or 1,500 fathoms 
with recovery of the 34 Ibs. sinker, may be executed 
with only the detention of stopping the ship, keep- 
ing her stopped for a quarter of an hour or twenty 
minutes while the lead is going down, and then 
going a-head full speed as soon as it has struck 
the bottom. 


A question has been asked with reference to 
flying soundings, as to the allowance to be made 
for the non-verticality of the wire. I have indicated 
that these are only approximate soundings, but 
they are sufficiently near for many practical pur- 
poses, and a little experience gives data for making 
allowances with considerable accuracy. [This was 
demonstrated by a diagram on the board. 1 ] With 
the aid of a little experience of what the wire really 
does in moving through the water in flying sound- 
ings, you may obtain very close results. In the 
Hooper, I believe, the flying soundings in from 
170 to 40 fathoms were ascertained within from 
10 per cent, to 3 per cent, of the actual depth. 

I hope my friend Mr. Froude may be induced to 
take up the subject of the resistance of the water 
against steel wire. He has apparatus at Torquay 
by which he measures the resistances experienced 
by models of ships, which I think might also be 
applied to the measuring of resistances experienced 
by wire, and from that some valuable results might 
be obtained. I have found the resistance in towing, 

1 This demonstration is given in a note on " Flying Soundings " 
appended to the present article. 


at seven or eight knots, 1,500 fathoms of piano- 
forte wire, with ring, short hemp line, and 30 Ibs. 
sinker at the end, is quite manageable. 

In reply to Mr. Gray, I may state that we 
brought up specimens of the material of the 
bottom by means of a tube fitted simply with a 
common door-hinge valve. The tube came up full 
of mud where the material was soft. There are a 
great many different plans of doing this, but we 
found no difficulty in getting specimens of the 
bottom with this tube and simple valve. 



APPROXIMATE soundings of great use, both in 
cable laying and in ordinary navigation, may be 
obtained in depths of 200 fathoms, or less, with re- 
markable ease, without reducing the speed of the 
ship below five or six knots, even when the wire is 
being paid out. For this purpose let the weight fall 
direct from the wire wheel over the taffrail, with a 
brake-resistance of from five to ten pounds. The 
moment of its reaching the bottom is indicated by 

VOL. ill. U i>, 


a sudden decrease in the speed of rotation of the 
wheel. The moment this is observed, a man 
standing at the wheel grasps it with his two hands, 
and stops it. Not more than three or four hundred 
fathoms of wire having run out, the hauling-in is 
easy. In following this process I have generally 
found it convenient to arm the lead with a proper 
mixture of tallow and wax, in the usual manner, to 
bring up specimens from the bottom. The actual 
depth is, of course, less than the length of wire run 

FIG. 45. Flying Soundings. 

out. The difference, to be subtracted from the 
length of wire out to find the true depth, may be 
generally estimated with considerable accuracy 
after some experience. The estimation of it is 
assisted by considering that the true depth is 
always, as we see from the annexed diagram, 

greater than / a and less than </P a 2 , where / 
denotes the length of wire out, and a the space 
travelled by the ship, diminished by the space 


travelled horizontally by the sinker during the 
time of its going to the bottom. 

The contrast between the ease with which the 
wire and sinker are got on board from a depth of 
200 fathoms by a single man, or by two men, in 
this process, and the labour of hauling in the ordi- 
nary deep-sea lead and line, by four or five men, 
when soundings are taken in the ordinary way 
from a ship going through the water at four or five 
knots in depths of from 30 to 60 fathoms, is 
remarkable. Professor Jenkin and I found this 
process of great value on board the Hooper, during 
the laying of the Western and Brazilian Telegraph 
Company's cables between Para, Pernambuco, 
Bahia, and Rio Janeiro. I am now having con- 
structed, for the purposes of navigation, a small 
wire wheel of 12 inches diameter, to have 400 
fathoms of pianoforte wire coiled on it, for flying 
soundings in depths of from 5 to 200 fathoms, 
without any reduction of the speed of the ship, or, 
at all events, without reducing it below five or six 

B B 2 




IT consists of a wire drum mounted on a 
galvanised iron frame, and a box to keep it in 
when out of use. The drawing Fig. 46 shows the 
machine with the frame carrying the wire drum 
lifted out of a box and resting on the supports 
in the position for taking a cast. 

The wire is coiled on a V-shaped ring A. This 
ring A can revolve independently of the spindle, or 
it may be clamped to the spindle by means of the 
plate BB. When the machine has been lifted and 
placed in the position shown in the drawing, the 
handles should be shipped and fixed by tightening 
up the thumb screw F. The arm C should then 
be turned round till it is behind the upright of the 
frame, and the catch D turned over to prevent the 
arm C turning. To put on the brake, turn the 
handle in the direction for winding in the wire ; 
to take off the brake and allow the wire to run out, 
turn the handle in the direction for paying out the 
wire. Half a turn, or at most one turn, of the 
handle in the direction for paying out is sufficient 
to release the wire drum and allow the wire to run 
out with the weight of the sinker hanging on the 
wire. While the wire is running out the handle 



FIG. 46. Navigational Sounding Machine.- 


should be held fixed in the hand, and as soon 
as the sinker touches the bottom, the handle 
should be turned in the direction for winding in, 
so as to put on the brake and prevent any more 
wire running out. When the brake has been put 
on and the egress of the wire stopped, turn over 
the catch D to release the arm C and wind in the 
wire. It will be observed that the arm C is held 
in the fixed position during the whole time except 
when the wire is being wound in. While the wire 
is coming in the arm C is allowed to turn round 
with the drum and spindle. 




THE Depth-Recorder is shown at 
Fig. 47. It is attached to the cover 
of the sinker by means of a short 
chain, from the ring at the top. 
When a cast is to be taken the 
Recorder is put inside the sinker 
and is supported by the pressure 
of the side springs against the in- 
side of the sinker ; the slack chain is 
put in on the top of the Recorder. 
The object of the side springs is to 
prevent the shock, which the sinker 
experiences when it strikes the bottom, 
from affecting the reading of the 
Depth-Recorder. When the sinker 
strikes the bottom, the Depth-Re- 
corder slips down the inside of the 
sinker and is thus relieved of the 
sudden shock. 

As the sinker descends, the in- 
creased pressure forces the piston D 
up into the tube while the spiral 
spring pulls the piston back. The 
amount that the piston is forced up 


against the action of the spiral spring depends on 
the depth. To record the depth the marker C is 
used. As the Recorder goes down the marker is 
pushed along the piston. When the Recorder is 
brought up to the surface of the water the piston 
comes back to its original position, but the marker 
remains at the place on the scale to which it was 
pushed, and shows the depth to which the Recorder 
has been. The depth is read off by the cross wire 
of the marker. 

Between each cast the nut A should be un- 
screwed to slacken the valve B, and the Recorder 
should be turned upside down to empty out an)' 
water which may- have leaked in. A little water 
in the upper bottle will not interfere with the 
accuracy of the indications of the Recorder. It 
may not be found necessary to empty the bottle 
every time. Make sure before each cast that the 
screw A is firmly screwed up. 

Occasionally a little grease should be pushed up 
the piston into the tube to keep the leather 
packing of the piston in good order. 

The sinker with the Depth-Recorder, ready for a 
cast, should always be kept bent on to the rope. 
The rope comes out of the box through a notch 
cut for the purpose. The sinker should be 
made fast in a convenient position close to the 



[Extracts from paper read, and illustrated by apparatus 
exhibited, before United Service Institution, February 4, 

THE machine before you is designed for the 
purpose of obtaining soundings from a ship running 
at full speed in water of any depth not exceeding 
100 or 150 fathoms. The difficulties to be over- 
come are twofold ; first, to get the lead or sinker 
to the bottom ; and, secondly, to get sure evidence 
as to the depth to which it has gone down. For 
practical navigation a third difficulty must also be 
met, and that is to bring the sinker up again, for, 
although in deep-sea surveys in water of more than 
3,000 fathoms depth it is advisable, even when 
pianoforte wire is used, to leave the thirty or forty 
pound sinker at the bottom, and bring back only 
the wire with attached instruments, it would never 
do in practical navigation to throw away a sinker 
every time a cast is taken, and the loss of a sinker, 
whether with or without any portion of the line, 
ought to be a rare occurrence in many casts. The 
first and third of these difficulties seem insuperable, 
at all events, they have not hitherto been over- 
come, with hemp rope for the sounding line, except 
for very moderate depths, and for speeds much 


under the full speed of a modern fast steamer. It 
may indeed be said to be a practical impossibility to 
take a sounding in 20 fathoms from a ship running 
at 1 6 knots, with the best and best-managed ordin- 
ary deep-sea lead. Taking advantage of the great 
strength, and the small and smooth area for re- 
sistance to motion through the water, presented by 
pianoforte wire, I have succeeded in overcoming 
all these difficulties ; and with such a sounding 
machine as that before you the White Star liner 
Britannic (Messrs. Ismay, Imrie, and Co., Liver- 
pool), now takes soundings regularly, running at 16 
knots over the Banks of Newfoundland and in the 
English and Irish Channels in depths sometimes as 
much as 130 fathoms. In this ship, perhaps the 
fastest ocean-going steamer in existence, the 
sounding machine was carefully tried for several 
voyages in the hands of Captain Thompson, who 
succeeded perfectly in using it to advantage ; and 
under him it was finally introduced into the service 
of the White Star Line. 

The steel wire which I use weighs nearly \\ Ibs. 
per 100 fathoms, and bears when fresh from 230 to 
240 Ibs. without breaking ; its circumference is only 
"03 of an inch. By carefully keeping it always, 
when out of use, under lime water 1 in the galvanized 
iron tank prepared for the purpose, which you see 
before you, it is preserved quite free from rust, and, 

1 The use in the newest machines of galvanized steel wire renders 
this precaution unnecessary. 


accidents excepted, this sounding line might out- 
live the iron plates and frames of the ship. If the 
sinker gets jammed in a cleft of rock at the bottom, 
or against the side of a boulder, the wire is inevit- 
ably lost. Such an accident must obviously be very 
rare indeed, and there does not seem to be any 
other kind of accident which is altogether inevitable 
by care in the use of the instrument. The main care 
in respect to avoidance of breakage of the wire may 
be stated in three words beware of kinks. A 
certain amount of what I may call internal molecu- 
lar wear and tear will probably occur through the 
wire bending round the iron guard rod which you 
see in the afterpart of the instrument, when, in 
hauling in, the wire does not lead fair aft in the 
plane of the wheel, as is often the case even with 
very careful steering of the ship ; but, from all we 
know of the elastic properties of metals, it seems 
that thousands of casts might be taken with the 
same wire before it would be sensibly weakened by 
internal molecular friction. Practice has altogether 
confirmed these theoretical anticipations so far as 
one year of experience can go. My sounding 
machine has been in regular use in charge of 
Captains Munro and Hedderwick in the Anchor 
liners AncJioria and Devonia (Messrs. Hender- 
son Brothers, Glasgow), for twelve months and 
seven months respectively, and in neither ship has 
a fathom of wire been lost hitherto, though 
soundings have been taken at all hours of day 


and night at full speed in depths sometimes as 
great as 120 fathoms. No break, not explicable 
by a kink in the wire, has hitherto taken place in 
any ship provided with the sounding machine. 
That it will bear much rough usage is well 
illustrated by one incident which happened in a 
cast taken from the Devonia, running at 13 
knots. The sinker in falling from the wheel into the 
water accidentally fell between the rudder chain 
and the ship, and 50 fathoms or so had gone out 
before it was noticed that the wire was running 
down vertically from the wheel instead of nearly 
horizontally as it ought to have been by that time. 
The handles were immediately applied to the 
sounding wheel, and it was turned round to haul in 
without reducing the speed of the ship. Though 
the wire was bent nearly at right angles round the 
chain until it was nearly all in, it was all got safely 
on board, as was also the cod-line with attached 
depth gauge, and the sinker at the end of it. 

When soundings are being taken every hour or 
more frequently (as in the case of a ship feeling her 
way up Channel from the 100 fathom line when the 
position is not known with sufficient certainty by 
sights and chronometers) the sounding wheel should 
be kept in position, with depth gauge, and sinker 
all placed ready for use. 1 With such arrange- 

1 The following instruction is printed on an enamel plate on the 
box containing the machine. Its observance is of the greatest 
importance to prevent ships from ever getting into positions where 


mcnts, and methodical practice, as part of regular 
naval drill in the use of the sounding machine, one 
minute of time, or from that to four minutes, suffices 
to take a sounding. 

A description of the machine and rules for its 
use are given in my printed paper of instructions. I 
have only now to add a few words regarding the 
depth gauge. Erichsen's self-registering sounding 
lead (patented in 1836) depending on the compres- 
sion of air might be used with my machine, but the 
simpler form before you is preferable as being surer. 
It too depends on the compression of air, but in it 
the extent to which the air has been compressed is 
marked directly on the interior of a straight glass 
tube by the chemical action of sea water on a 
preparation of chromate of silver with which the 
tube is lined internally. Between the salt of the 
sea water and the chromate of silver a double 
decomposition takes place. The chlorine leaves the 
sodium of the common salt and combines with the 
silver, while the chromic acid and oxygen leave the 
silver and combine with the sodium. Thus chloride 
of silver, white and insoluble, remains on the glass 
in place of the orange-coloured chromate of silver 
lining as far up as the water has been forced into 
the tube, and the chromate of sodium dissolved in 

there can be clanger of shipwreck by running on rocks or on shore. 


the water is expelled as the air expands when the 
tube is brought to the surface. 

My navigational sounding machine was brought 
into practical use for the first time in the steamship 
Palm, belonging to Messrs. Charles Horsfall & Co., 
Liverpool, in a voyage to Odessa and back about a 
year ago, in command of Captain E. Leighton. I 
cannot illustrate the use of the machine better than 
by reading to you an extract from a letter I received 
last April from Captain Leighton, describing his 
experience of it in this first trial : 

" During the voyage in the Palm steamship, 
which has just come to an end, I took frequent oppor- 
tunities of testing the sounding machine when I had a 
chance of cross-bearings to verify the depths as 
shown by chart, and always found it most accurate. 
For instance, going up through the Archipelago and 
just after clearingthe Zea Channel, I got a good posi- 
tion by bearings, chart showing 79 and 76 fathoms, 
two casts of your glass gave 78 and 75 fathoms. 
In the Bosphorus also it gave capital results in 
30 to 40 fathoms water. 

"The first real use I made of the machine was in 
the Black Sea during a fog which obscured every- 
thing. Wishing to make sure of my position I 
put the ship's head for the land, and kept the 
machine at work. After running in to 30 fathoms 
at full speed I slowed down and went in to 12 
fathoms, then hauled out to a convenient depth 
and put her on the course up the coast. When it 


became clear I found myself in a proper position, 
and no time had been lost by stopping to sound. 

" Ho"- many shipmasters let hours go by without 
obtaining soundings, either because of the delay 
or on account of the danger of rounding-to in 
heavy weather to get them, when, if they were 
provided with your sounding machine they could 
have their minds set at ease by having timely 
warning of danger, or by knowing that they \vere 
in a good position ! " 

I had myself very satisfactory experience of the 
usefulness of the sounding machine in coming up 
Channel, running before a gale of south-west wind 
in thick weather, on the 6th and /th of last August, 
on returning from Madeira in my yacht Lalla 
Rookk a small sailing schooner of 126 tons. 
About 5 A.M. on the 6th, I took two casts, and 
found 98 fathoms (sand and red spots) and 101 
fathoms (sand and small shells). The mean \vith 
a correction of 2\ fathoms to reduce to low water, 
according to the state of the tide at Ushant at the 
time, was 97 fathoms. Thenceforward I took a 
sounding every hour till eight in the evening. By 
writing these soundings on the edge of a piece of 
paper at distances equal according to the scale of 
the chart to the distances run in the intervals, 
with the edge of the paper always parallel to the 
course, according to the method of Sir James 
Anderson and Captain Moriarty, I had fixed 
accurately the line along which the vessel had 


sailed, and the point of it which had been reached, 
with only a verification by a noon latitude. At 
6 o'clock next morning, by the soundings and 
course, with proper allowance for the flood-tide, I 
must have been about thirteen miles magnetic 
south of the Start, but nothing of the land was to 
be seen through the haze and rain ; and with the 
assistance of about ten more casts of the lead (by 
which I was saved from passing south of St. 
Catherine's) I made the Needles Lighthouse right 
ahead, at a distance of about three miles, at 2 P.M., 
having had just a glimpse of the high cliffs east of 
Portland, but no other sight of land since leaving 
Madeira and Porto Santo. In the course of the 288 
miles from the point where I struck the 100 fathom 
line, to the Needles, I took about thirty casts in 
depths of from 100 fathoms to 19 fathoms without 
once rounding-to or reducing speed. During some 
of the casts the speed was ten knots,, and the 
average rate of the last 220 miles was a little over 
nine knots. The accompanying chart is copied 
with reduction of five to one from the working 
chart (Admiralty chart of the English Channel, 
1598) which I used for the last two days of the 
voyage. It shows only two changes of direction 
one made at 5 A.M. on August /th, to make sure of 
not getting too close in by the Start as the weather 
was very thick ; and the other at noon of August 
7th, to get into 15 fathoms to make the Needles. 
The places of all the casts are show r n, and the 




C C 


depths found in each, case except the cast at 9 A.M. 
on the 6th, and all but one of the last ten casts. 

It is a pleasure to me to be able to add, that the 
sounding machine has also been successfully used 
in the Royal Navy. Admiral Beauchamp Sey- 
mour and Captain Lord Walter Kerr having kindly 
taken it on board H.M.S. Minotaur for trial last 
summer, Lord Walter Kerr, on his return from 
Vigo, wrote regarding it as follows : 

" The sounding machine is most serviceable, 
We have been using it constantly when running 
up Channel, from the time of crossing the line of 
soundings to the time of reaching Plymouth ; and, 
though running before a gale of wind, with a heavy 
sea, at the rate of ten knots, we were able to get 
soundings as if the ship had been at anchor. We 
were able to signal to the squadron each sounding 
as it was obtained ; thus, in thick weather, verifying 
our position by soundings without having to round 
the ships to." 

\Extract from Printed Instructions for the Use of Sir 
William Thomson's Navigational Sounding Machine^ 

Regular Use of the Machine. WlIEN NAVIGAT- 


THE SPEED OF THE SHIP. It takes from a few 
seconds to a minute for the sinker to reach the 
bottom from the time it is let go, and from a 
quarter of a minute to four minutes for two men 
to haul it in, if the depth is from 10 fathoms to 100 
fathoms. (One man can haul it in though the ship 
be running at 16 knots, but not quite so quickly 
nor so uniformly as two.) Thus, it is easy to take 
a sounding every ten minutes, with an extra hand 
or two to relieve. Two men can with ease take a 
sounding every quarter of an hour, and this should 
be the rule whenever in keeping the machine thus 
going useful information as to the ship's place can 
be had. It is not necessary to use a tube every 
time. The reading shown on the counter at the 
moment the sinker strikes the bottom allows you to 
judge the depth surely and accurately enough if you 
use a tube occasionally. The reading on the counter 
shows approximately the number of fathoms of 
wire run out. 1 This may be something nearly 

1 Two turns of the wheel give about a fathom of wire ; but this 
differs a little according to the quantity of wire on the wheel, and 
therefore if for any purpose, as for instance taking an up-and-down 
cast, which may be done in 300 fathoms water or anything less, 
with the wire ordinarily supplied on the wheel, the counter reading 
must be corrected according to actual measurements of the circum- 
ference of the wire-wheel when the sinker is at the bottom and 
when the wire is wound on again. 

C C 2 


twice the depth ; but the proportion of wire to 
depth differs according to the depth, the speed of 
the ship, and the roughness of the sea. For the 
first of a set of casts use a tube and read off the 
depth by applying it to the scale of fathoms. 
After three or four more casts use another tube, 
and then, according to judgment, use a tube as 
frequently as is necessary to check your inferences 
of depths from the counter readings. The char- 
acter of the bottom brought up on the arming of 
the sinker is of course to be examined every time. 


\Paper read at the Naval and Marine Exhibition, 
Glasgow -, February nth, 1881.] 

FOR a lighthouse to fulfil the reason of its 
existence, it must not only be seen, it must be 
recognised when seen. If seen, and not known, a 
lighthouse is of no use ; if not seen, it certainly 
could not be of use. There has been much of 
discussion as to what is the primary and most 
important quality of a lighthouse. Penetrative 
power to allow the light to be seen in thick weather 
at as great a distance as possible is, of course, the 
first object to be striven for. The next question is 
How to make use of a lighthouse when seen ? 
If a sailor descrying a lighthouse from a great 
distance is in doubt whether the light is on a 
fishing-boat a mile off, or on the masthead of a 
steamer three miles off, or on a lighthouse six miles 


off, it is obvious that the lighthouse in merely 
letting its light be seen, had achieved but a small 
part of the task to be achieved. I do not want to 
take the "ungracious part of criticising or saying 
anything has been done less well than it should be 
done ; nor do I want to be behind in expressing my 
cordial and most sincere admiration of the great 
work which has been done for the world by the 
lighthouse boards of this country by the Trinity 
Board, the Board of Northern Lights, the Commis- 
sioners of Irish Lights, and, not least in intensity, 
if not so great as the others in quantity, of good 
done, by the Clyde Navigation Trustees. But I 
must say that there has not been among lighthouse 
authorities hitherto quite enough of determination 
to make the very most of the distinctive character 
and the possibilities of giving a distinctive character, 
to their lights that science and common-sense 
placed before them. There is too much, perhaps, 
of the idea of saving oil, or of making a certain 
quantity of oil go a great way, and not quite 
enough of the idea that the object of the lighthouse 
after all is to be known, and that to be seen without 


being known is not enough. The question to be 
considered is how to know one light from another 
how to know a light descried just above the 
horizon, and dipping now below the horizon, lost 
sight of for a quarter of a minute, again seen, lost 
for a little time, and again seen continuously to 
recognise it with certainty, and without loss of time, 
in such circumstances. The Holywood Bank Light 
in Belfast Lough, the leading light for vessels enter- 
ing the Lough, is so recognised, being a short-short- 
long eclipsing light. The Copeland Light off the 
south entrance of Belfast Lough is not recognisable 
by any distinguishing characteristic, being merely a 
fixed light. It has, however, I am informed, been 
determined by the Commissioners of Irish Lights to 
alter it, and give it a distinctive character. I take 
those two cases because, when a celebrated 
lighthouse engineer was with me on one occasion 
in my yacht, approaching Belfast in the small hours 
of a summer morning, we had just that experience 
of them both. I said to him, " Look at that light 
and tell me what it is ; is it a masthead light, or 
what is it ?" He could not tell. It was the 


Copeland Light, as we learned soon afterwards from 
our position. My friend fully admitted after that, 
what he never admitted before namely, that it was 
possible to confound a lighthouse light with a light 
on a steamer's masthead ; and soon after, the 
Holywood Bank, barely visible ten miles off, was 
recognised by its short-short-long within a quarter 
of a minute of its being first seen, and gave a 
triumphant proof of the practical value of its 
distinctive character. 

With reference to the description of lights and 
their distinctions in lighthouses, there is, in the first 
place, to be considered the character 'of the light, and 
the appliances for economizing of it. The old coal 
fire on, the cliff, which was the first lighthouse, was 
a relic of the past, which would never now be set 
up for the purpose of marking a point on the coast ; 
yet, practically, where there are blazing furnaces at 
ironworks, as on the Ayrshire coast in the neigh- 
bourhood of Ardrossan, these same fires do 
constitute very important, though undesigned 
marks by which a mariner discovers his position. 
The substitution of economical lamps, in which a 


great deal of light was given with a moderate 
consumption of fuel, took the place of the coal fires 
on the cliffs. Then reflectors were introduced. A 
great invention was made early this century, which 
led to the now prevailing dioptric system. It is 
perfectly clear that the great brilliance and success 
in economizing the fuel of the flames in the light- 
houses of the present day is directly due to the 
invention of the dioptric system ; and has been 
largely promoted by the great use made of it, and 
the great improvements effected on it, by Messrs. 
Stevenson, the engineers of Northern Lights. 
Then came the question of how to economize light 
when not wanted to show all round, as, for instance, 
in the case of the Lamlash Light, which shows a 
brilliant light seaward, and a moderately-bright light 
over the Bay of Lamlash. The occulting light 
shown by the Messrs. Stevenson in our present 
Exhibition is a light fulfilling one of the conditions 
of characteristic quality, with very perfect 
economy of light. The very principle by \vhich 
light was economized has given one of the first 
lighthouse characteristics in the ordinary revolving 


light. Not content with condensing the light to the 
horizon so as to shed itself out in all horizontal 
directions, engineers condensed it into certain fixed 
directions for special reasons. Sometimes they 
condensed the light into a ray, for the reason of 
sending it in the direction of a particular channel : 
sometimes for the sake of giving greater intensity 
than they could practically attain otherwise, and 
then they made the ray revolve so as to shed its 
brightness all round the horizon in the period of its 
revolution. A policeman's bull's-eye lantern is an 
instance in point. There is a greater intensity of 
light in a ray from an ordinary bull's-eye lantern 
than a light of anything like the same power could 
give without that optical appliance, or something 
equivalent to it, or more perfect than it. 

Besides its light, a modern lighthouse generally 
contains also, for use in such thick or foggy 
weather that the light cannot be seen, a sound- 
making appliance, the object of which is not only 
to be heard, but when heard to be immediately 
recognised to be itself and nothing else. Mr. Price 
Edwards, in his communication to the Society of 


Arts, of 1 5th December last, on "Signalling by 
means of Sound," gave an interesting and clear 
description of the chief practical methods hitherto 
in use for this exceedingly important addition to the 
efficiency of lighthouses ; and I shall have occasion 
to return to the subject of characteristic sounds in 
relation to the several methods which have been 
adopted to give characteristic qualities to the light 
itself of a lighthouse. 

Setting aside colour now generally admitted to 
be indefensible, as a distinction for lighthouse lights, 
except in the proper use of it, which is to distinguish 
different directions of the light by coloured sectors 
to mark rocks or other dangers, or the safe limits 
of navigable channels we find all the characteristic 
qualities of lighthouses to come under one or other 
of the following three descriptions : 

I. Flashing lights. 
II. Fixed lights. 
III. Occulting or eclipsing lights. 

The well-known name " Revolving lights " is 
habitually limited to flashing lights ; but it is liable 
to ambiguity, because the same revolving mechan- 


ism is also applied in many cases to produce the 
eclipses of " Occulting or eclipsing lights." The 
official description of the revolving light in the 
" Admiralty List of Lights," is as follows : 

" Rev. Revolving light, gradually increasing to 
full effect, then decreasing to eclipse. [At short 
distances and in clear weather a faint continuous 
light may be observed.] " 

This, in fact, includes the description of the 
flashing light : 

" Fl. Flashing showing flashes at short inter- 
vals, or groups of flashes at regular intervals." 

A combination of the fixed and flashing qualities, 
though comparatively rare, constitutes an important 
characteristic light, described in the Admiralty list 
as follows : 

" F. and FL Fixed light with addition of white 
or coloured flashes, preceded and followed by a 
short eclipse." 

Thus we have really very little of complexity in 
the fundamental classification into the three 
descriptions of Flashing Fixed, and Occulting. 

In the flashing light, the light is visible for only 


a short time a fraction of a second, or from that 
to five or six seconds and then disappears ; and, 
for a much longer time than the duration of the 
flash, it remains invisible, until it again flashes out 
as before. In the fixed light there is no dis- 
tinguishing characteristic whatever, but merely a 
light seen shining continuously and uniformly, 
The occulting light is visible during the greater 
part of its time like a fixed light, shining continu- 
ously and uniformly. Characteristic distinction is 
given by a short eclipse, or by a very rapid group 
of two or three short eclipses, or of short and 
longer eclipses recurring at regular periods, " flashes 
of darkness," as they have been called, cutting out, 
as it were from the light its mark, by which it may 
be distinguished and recognised to be itself and 
nothing else, in the very short time (from half- 
second at the least, to seven seconds at the most) 
occupied by the group of eclipses. 


Six years ago, in every flashing light there was 
just one flash in the period, and thus the length of the 


period was the sole distinction between one flashing 
light and another. Thus, in the " Admiralty List 
of Lights for the British Islands " for 1875, we find 
about 100 flashing lights of different periods, from 
the four-seconds' period of Ardrossan Breakwater 
Light to the two-minutes' period of the upper light 
of Lundy Island, of the South Stack, Holyhead, 
and of one of the lights on Slyne Head, off the 
west coast of Ireland ; and the distinction of each 
one of these 100 lights was solely its period as a 
simple flashing light, except in cases in which the 
objectionable distinction by colour was put in 
requisition. When it was determined to choose 
periods the same, or nearly the same, for neigh- 
bouring lights, it was found necessary to add 
distinction by colour, objectionable as this is if not 
enforced by necessity. Thus, for example, the 
Gull Stream lightship, in the fairway between the 
Goodwin Sands and the Kentish Coast, is a 
revolving light of twenty seconds' period, while the 
East Goodwin lightship, about six miles from it, is 
a revolving light of fifteen seconds' period. With- 
out greater accuracy than is generally to be found 


in the time-keeping of flashing lights, even on 
shore, the distinction between fifteen and twenty 
seconds could scarcely be relied upon as given by 
the mechanism ; and even if given trustworthily by 
the mechanism, the distinction could only be 
discovered by the sailor with certainty by the aid 
of a chronometer, the use of which is out of the 
question as a practical means for recognising a 
light when seen. To give sufficient distinction 
between these two lights, therefore, it was found 
necessary to use colour; the East Goodwin was 
made green, the Gull Stream white. Again, the St. 
Agnes Light, Scilly, and the light on the Wolf Rock 
two far outlying lights, about twenty miles asunder, 
are each of them of half a minute period from flash 
to flash, and the sole distinction between them is 
that the flashes of the Wolf Light are alternately 
white and red, while those of the St. Agnes' Light 
are all white. 

The insufficiency of the distinction of flashing 
lights, merely by length of period, had come to be 
felt so strongly that a very important fresh dis- 
tinction was introduced in 1875, in the lightship 


then first placed on the Royal Sovereign shoal ; 
the Group Flashing Light of Mr. Hopkinson, in 
which, instead of just one flash in the period, there 
are, in the case of the Royal Sovereign Light, three 
flashes in the period, or, as may be in other cases, 
two flashes, or four flashes, the interval between 
the successive flashes of the group being much 
shorter than the interval from group to group in 
the whole period. In two cases in the English 
Channel, the North Sand Head and the Casquets, 
the new triple flashing light was introduced to 
replace, by a group of three flashes in rapid 
succession, three separate lights which had been the 
characteristic arrangement previously ; three fixed 
lights in the case of the North Sand Head, and 
three simple flashing lights in the case of the 

Mr. Preece has imprudently pointed out that Mr. 
Hopkinson's triple flashing light is the letter S of 
the Morse-Colomb flashing alphabet. Sailors, we 
may hope, are happily ignorant of this truth, 
otherwise the proverbial captain of the collier 
would be calling out to his chief officer " Bill, was 


that a S, or a I, or a H, or a E ? " Bill, if he was 
well up in dramatic literature, would reply, 
" Captain, them is things as no fellow can under- 
stand." I must say, however, that I agree with Mr. 
Preece, and think that, while many may find 
memory aided, none can be embarrassed, by an 
official statement of the Morse letter corresponding 
to any group of flashes or eclipses that may be 
chosen as the characteristic for any particular light. 
This, however, is a matter of comparatively small 
moment at present. The great thing is to find how 
lights may be most surely and inexpensively 
rendered distinctive, so that no sailor, educated or 
uneducated, highly intelligent or only intelligent 
enough to sail a collier through gales, and snow- 
storms, and fogs all winter between Newcastle and 
Plymouth, may know each light as soon as he 
sees it, without doubt or hesitation. 

This object is fully attained by the triple flashing 
light, if quick enough. The triple flashing light of 
the Casquets, and of Bull Point (Bristol Channel) 
which are the quickest of the kind hitherto made, 
complete their three flashes in twelve seconds, after 



which there is an interval of eighteen seconds of 
darkness. These are, no doubt, very admirable and 
thoroughly distinctive lights ; but it would be very 
much better if they were made three times as fast, 
which, with the existing machinery, could, I believe, 
be easily done. If this were done they would 
show their flashes each in two-thirds of a second, 
and with only a second of time between. Thus, 
the three flashes completed in four seconds would 
be instantly recognised as a group of three, without 
the necessity of any counting either of flashes or of 
numbers of seconds of time in the intervals between 
the flashes ; and, instead of having to wait in 
darkness for eighteen seconds, the sailor would 
only have to wait six seconds for a repetition of 
the triple flash. 

The Royal Sovereign, the Seven Stones, the 
Newarp (near Yarmouth, on the east coast), and 
the Saltees (off the south coast of Ireland), all 
lightships supplied within the last few years with 
the Triple Flashing Light, are each of them of one 
minute period, of which there is thirty-six seconds 
of darkness, and twenty-four seconds of flashing. 


These lights are all too slow to do full advantage 
to the triple flash system. When one of them is 
first seen, it is very apt to be confounded with an 
ordinary "revolving light" that is, a single-flash 
flashing light. Even somewhat careful watching 
at all events if the weather or the distance from the 
light be such as to leave any room for doubt does 
not always immediately resolve the doubt. A 
sixfold quickening of each of these lights would 
greatly enhance its distinctive quality, and would 
make it really fulfil the condition pointed out by 
the Elder Brethren of the Trinity House, as the 
object to be aimed at in every modern lighthouse, 
" That he that runs may read." 

The satisfactory distinctions of group-flashing 
lights are exhausted in the groups of two or three 
or four flashes ; because, to count five or six, or 
more, would be embarrassing and liable to mis- 
take at sea. It has been proposed to obtain 
further distinction by using groups of longer and 
shorter flashes, as in Captain Colomb's Flashing 
Telegraph, now in general use, and very thoroughly 
appreciated both in the Navy and in the Army ; 

D D 2 


but there are optical difficulties in the way of 
making, with satisfactory economy, groups of long 
and short flashes, separated by short intervals of 
darkness in the group, and comparatively long 
intervals of darkness between successive groups ; 
and considering how very much more useful and 
satisfactory at sea is a lighthouse showing long 
light with short intervals of darkness than even the 
quickest of flashing lights, it does not seem desir- 
able to push the distinctions of flashing lights 
further than the double, triple, and quadruple 
groups. The periods for these lights which seem 
best adapted for practical purposes, all things con- 
sidered, but most particularly their value to the 
sailor, are as follows : 

Number of flashes 
in period. 

Duration of 
each flash. 

Duration of 



i sec 


2 sec 



i t 









Three .... 








It may be objected to the suggestions of the 


preceding table, that the quarter-second flashes are 
too short to be perceived with the same certainty 
as flashes of five or six seconds' duration. Experi- 
ment alone can answer decisively the question 
whether, with equal maximum brilliancy in each 
flash, a flash of quarter-second duration recurring 
every two seconds, or one of half-second recurring 
every four seconds, or one of one second recurring 
every eight seconds, is the most easily to be seen 
at a great distance or in hazy weather. From 
physiological experiments already made, it has been 
concluded that one-tenth of a second is a long 
enough time to fully excite the sensibility and 
perceptive power of the eye, and it seems probable 
that rapidity of recurrence of the contrasts between 
light and darkness will give a positive advantage to 
the quicker flash in respect to perceptibility, even 
when the observer knows in what direction to look 
for the light ; and when he does not know exactly 
in what direction to look, which is the practical case 
of a sailor at sea trying to pick up a light, shortness 
of the time of invisibility is of supreme importance. 
All things considered, it seems most probable that 


the quarter-second flash recurring every two seconds 
will be very much more easily and surely picked up 
practically at sea than a flash of one second recur- 
ring every eight seconds. 

Before passing from this subject of flashing lights, 
I may be allowed to say that I first received my 
impression of the vital importance of quickness in 
a light from a very practical man the man who, in 
1866, showed us within a quarter of a mile, in mid- 
ocean, where to find the cable which had been laid 
and lost in 1865 Captain Moriarty, R.N. I well 
remember when on one occasion, either in 1858 or 
1865, I do not know which, in making the Irish 
coast in dirty weather, he said 

"Those lighthouses should flash out their 
characters like your electric signals ; every light- 
house should flash, and flash, and flash, many times 
in a minute, showing you which lighthouse it is 
every time. That long minute of the revolving 
light has often seemed to me like an age, when I 
have been anxious to make out where we were in a 
gale of wind and rain." 



Of the 623 lights numbered in the " Admiralty 
List of Lights for the British Islands for 1881," 490 
are fixed, 112 are flashing, and 21 are occulting 
(or "eclipsing," or "intermittent"); and similar 
proportions are to be found in the official list of 
lights for other parts of the world. Thus it 
appears that fixed lights constitute the great 
majority. The fixed light has a great advantage 
in respect to practical usefulness over the flashing 
light, in being always visible. The superior 
brilliancy produced by optical condensation of the 
revolving light is, in some respects, dearly bought 
economy, when the great diminution of usefulness 
to the sailor, in its comparatively long periods of 
darkness, is taken into account. Theorists who 
praise the revolving light unqualifiedly for its 
superior penetrative power seem to forget the 
counterpart in optics to the great principle in 
dynamics that which is gained in power is lost in 
speed : in flashing lights, what is gained in brilliancy 
is lost in time of visibility. The painfully anxious 


scanning of the horizon for a one-minute flashing 
light, is known to every one who has ever had 
occasion to look for one in practical navigation ; 
and the comparative ease of picking up a fixed 
light, and keeping sight of it when it is found, in 
difficult circumstances, is thoroughly appreciated at 
sea by sailors. Still, if the revolving light can be 
seen at all, whatever be the difficulty in picking it 
up, and whatever the annoyance of losing sight of 
it and having to pick it up again, it has fulfilled the 
object of a lighthouse. All are agreed in the 
maxim that " the grand requisite of all sea lights is 
penetrative power ; " and if the fixed light cannot 
be seen at a distance, or in weather in which the 
revolving light is seen, the fixed light has failed, 
and the revolving light has done its work for the 
occasion. It depends very much on the special 
circumstances whether the same quantity of light, 
given out uniformly as a fixed light, or condensed 
and given out in flashes, with comparatively long 
intervals of darkness, as in the revolving light, is 
better in respect to being seen. In stormy or 
variable weather, with heavy showers of rain or 


snow, the fixed light is much safer than a one- 
minute revolving light of much greater absolute 
brilliancy ; as several successive flashes of the 
revolving light may be lost through passing 
showers, while the fixed light loses no chance of 
being seen in intervals between the showers. On 
the other hand, in hazy or foggy weather of toler- 
ably steady character, a revolving light can be seen 
efficiently at a greater distance than the same 
absolute quantity of light, given out uniformly as a 
fixed light. 

In the question of economy, the great first cost 
of the optical apparatus, special to the revolving 
light, must be set against the greater consumption 
of oil, or gas, or fuel to obtain in a fixed light, 
whether it be an oil or gas lamp, or an electric light, 
the same brilliancy. In many cases, indeed, the 
interest of the money spent on prisms, and lenses, 
and mechanism in the revolving light, and in some 
of the most beautiful and perfect of the appliances 
for the azimuthal condensation of fixed lights, 
would supply the oil required to give the same, or 
nearly the same, brilliancy all round the horizon. 


These circumstances are, of course, all to be taken 
into account by the proper authorities in respect to 
every project for a new lighthouse. But we have 
actually at present the great fact of 490 fixed lights 
on the coasts of the British Islands ; and when it is 
considered desirable or necessary to give more 
brilliancy to any of them, this may not best be 
done by converting it into a flashing light, but by 
making it a more powerful oil or gas light, or 
converting it into an electric light. Indeed, after 
Mr. Douglas's communication of two years ago 
(March 25th, 1879) to the Institution of Civil 
Engineers, on " The Electric Light Applied to 
Lighthouse Illumination," and the discussion which 
followed upon it, and considering the great progress 
which has been made since that time in lighting by 
electricity, we can scarcely doubt that, in the 
course of a few years, nothing but the electric light 
will be thought of for any new lighthouse of the 
greatest importance. 

The great defect of fixed lights at present is the 
want of characteristic quality by which the sailor, 
when he sees a light which really is a lighthouse 


light, may immediately feel sure that it is so, and 
not a steamer's mast-head light, nor a trawler's or 
fishing-boat's light, nor a light on shore other than 
a. lighthouse light ; and that knowing it to be a 
lighthouse, he may know exactly which of two or 
more possible lighthouses it is. The need for 
thorough-going remedial measures to remove this 
defect has been more and more felt of late years, 
and is now very generally admitted. Unless a 
second light is to be added, or the generally 
objectionable expedient of colour for distinction is 
in any particular case to be admitted, the only 
systematic means of giving characteristic quality to 
a fixed light is by means of occupations or eclipses ; 
and hence the origin of the " Occulting " or 
" Eclipsing light." We may accordingly look 
forward to all, or nearly all, the important fixed 
lights of our coast being, without any very long 
delay, converted into lights of this class. It is 
satisfactory to find that during the last year the 
Elder Brethren of the Trinity House converted one 
most important light, that of the North Foreland, 
and another very important one, the light on the 

I : 2 SS .2 


I!!* 8 . 

T3 *O JS *J ^ E. 

I alia 
5 SJ I 

W t^. 


t^ M C^OO N Tt-vO M- N M vO N in N 
^vot^M-^-int^ O\ M.NcriTi-invo 
c?>cnro-<j--^-^-Tj- -^ inmminin in 


west end of Plymouth Breakwater, into eclipsing 
lights, and that a similar improvement has been 
promised for five more of the fixed lights under 
their charge (Mucking, Lowestoft, Chapman, 
Flatholm, and Evan) within the official year 
1 880- 1. 


The 22 eclipsing lights at present existing in the 
British Islands are described in the preceding Table 
(see page 412), extracted from the Admiralty List 
of Lights for iSSi. 1 

To these is to be added the Cardross Light on the 
Clyde, at present a red light, but which, before the 
end of next month, is to be converted into a white 
eclipsing light of the same character as the Craig- 
more light in Rothesay Bay, long-short-long-short. 
It was judged by the Trustees of the Clyde 

1 Since the publication of this List, it has been announced that 
the Chapman Light, on the Thames, is to be '''occulting, twice in 
quick succession every half-minute" which is the same as Garvel 
Point, on the Clyde, except that the period is half -a- minute, instead 
of the eight seconds period of Garvel Point. 


Navigation, under whose charge this light is, 
that the long-short-long-short would be thoroughly 
free from liability to be mistaken for the occult- 
ing light (short-short) off Garvel point, three miles 
from it, and would, in the circumstances, give it 
a more telling characteristic quality than a single 
eclipse in the period, or than any group of three 

It will be seen, from the preceding Table of 
occulting lights that, with the exceptions of Holy- 
wood Bank, Craigmore, Garvel Point, Chapman, and 
Cardross, the distinction in each case is only a single 
eclipse in the period, and that, except in nine of 
them, the period is one minute or upwards, but in 
all, except five, the duration of the eclipse is less 
than half a minute. In all the more recent eclipsing 
lights the period is half a minute or less, and the 
duration of the eclipse is at most five seconds. The 
tendency, undoubtedly, is to quicken the action still 
further, following the example of the old Point 
Lynus Light, with its eight seconds of visibility 
and two seconds of eclipse. 

The necessity for a very short period is not so 


urgent in the case of eclipsing lights as it is in the 
case of flashing lights. A long period in the case 
of a flashing light means a long period of darkness, 
throughout which the light is lost sight of. The 
inconvenience of a long period in an eclipsing light 
is merely the length of time during which the sailor 
may have to wait to know which light it is ; he 
never loses sight of the light except for the two 
or three seconds' duration of one of the eclipses. 
But quickness of each group is just as important to 
allow ready and sure identification of its character 
as is the quickness of a group of flashes in the 
group-flashing lights of which I have already 

The important question is now to be met How 
may eclipses be best arranged to give the requisite 
number of characteristic distinctions, for the large 
number of fixed lights on our coasts which need 
distinction, with as little as may be of interference 
with the valuable quality of fixity ? The answer, I 
believe, is by groups of eclipses described as 
follows : First one, two, three, or four very short 
eclipses say of not more than one second each 


separated by equal intervals of light in the group, 
and the groups of eclipses following one another 
after intervals of not less than eight seconds of 
undisturbed bright light ; next groups of two or 
three short and long eclipses, the short eclipse one 
second, the long eclipse three seconds, the interval 
of light between the eclipses of a group one second, 
and the interval of undisturbed light between the 
groups of eclipses not less than eight seconds. I 
fixed upon the time one second, because, after 
many trials of mechanisms to produce the eclipses 
I found that I could produce all the groups of 
eclipses at the rate corresponding to one second for 
the short eclipse by a simple and inexpensive 
machine applicable to any lighthouse, large or 
small, and of any variety of optical arrangement, 
whether merely with condensation to the horizon, 
or with the additional appliances required to con- 
dense into a particular azimuth. 

A machine fulfilling these conditions is now at 
work in the college tower of the University of 
Glasgow, performing the short-long-short of the 
following table for four hours every evening. It 


has been doing this for a month, and shows no 
signs of wear. Indeed, there is no part of the 
machine which is liable to wear in the course of 
years regular service in a lighthouse. I refer to 
this machine at present, because it has been supposed 
that the plan of mechanism used in the Holywood 
Bank, the Garvel Point, and Cardross Lights that 
is, a mechanism producing eclipses by revolving 
screens, and therefore applicable only to light 
without azimuthal condensation is the only 
mechanism which can practically produce the 
groups of eclipses at the speed necessary to carry 
out this method of giving characteristic qualities to 
fixed lights. The use of gas in lighthouses, 
whether for smaller lights visible to a distance of 
four or five miles, or for any more powerful lights 
such as the splendid lighthouses of Tuskar and 
Houth Bailey, is admirably adapted for the quickest 
systems of eclipses of from one half to three 
seconds' duration for giving distinctive character, 
although it has not been taken advantage of in 
this respect except in the small Craigmore Light in 
Rothesay Bay by Mr. Mortimer Evans. 
VOL. in. E E 


My proposal for giving character to fixed lights 
is at present definitely limited to the ten varieties 
shown in the following table the short eclipse 
being one second, the long three seconds, in every 
case, except the one-short and the long-short-long- 
short. In these the short eclipse is a half-second ; 
and the long eclipse is three half-seconds. 


i-g % 


<- < rt 
O C> 

^ 0) O 

fij 2 M 


2 w o> 

^ .S M -g 


Description of the eclipse. 


^g.S t< 

.S rt 71 
o> c v qj 

'o g ^^ 

5 .& 1 


*C o t^ _ 2 

p M o o 




3 seconds 

12 seconds 



A second 



Short-short . 

1 2 

Two ... 






T P 

Three .. 

Short- short-short 


1 J 

T C 

Three . 




Short-long-short . .... 







Four 1 .. 

Long short-long-short 



It is to be remarked that the times stated in the third and fourth 
columns need not be known or noted to let the light be recognised. 
The description in the second column, "short-short," for instance 

1 This characteristic is very easily read, and may be used with 
advantage in cases in which there is no practical difficulty in obtain- 
ing speeds corresponding to the times half-second and three half- 
seconds for the short and long eclipses. 


"short-long-short" or "one long" or "one short "as the 
case may be, suffices, and is intelligible to every one, learned or un- 
learned, and lets the light be recognised with the greatest ease. As 
to the distinction between "long" and "short," the contrast be- 
tween the two, following one of them instantly after the other, is 
unmistakable. The only cases of the preceding table in which 
there is not this contrast to show the distinction are the first and 
second ; but the half-second eclipse of case 2 cannot in practice be 
ever mistaken for the three-seconds eclipse of case I, which is six 
times as long. 

It is obvious this plan may be understood 
immediately by any person learned or unlearned, 
reading the description, or being told it by word of 
mouth, and that no knowledge of the Morse letters 
corresponding to ;he several groups of eclipses is 
needed. Indeed, if Mr. Preece and others had not 
let out the secret, I might have brought forward 
this proposal without any acknowledgment of 
indebtedness to Morse or to Captain Colomb, had 
I been disposed to omit to give credit where 
credit is due for very brilliant and valuable 
inventions, and had I thought only of the very best 
way of putting forward my little suggestion in the 
manner most likely to promote its early adoption 
by the lighthouse authorities. 

I have only to add, in conclusion, that the 

E E 2 


highly important suggestion of Sir Richard 
Collinson, to use a high and a low note in 
direct contrast, to give characteristic sounds for 
lighthouses, may be worked out systematically in a 
very convenient manner by using the combinations 
of the preceding table ; with a high note instead of 
the short eclipse, and a low note instead of the long 
eclipse ; the low note of the same duration as the 
high note ; the interval between the notes of each 
group about the same as the time of each blast ; 
and the interval of silence between the group of 
blasts much longer than the whole time of each 
group. When the fog-siren is used there is no 
difficulty in making the blasts as short as we please, 
and they certainly ought not to be longer than a 
half-second or three-quarters of a second. Quick- 
ness is here, as in many other nautical matters, of 
vital importance. Let any one try for himself, 
sounding a high and a low note in rapid succession, 
or two high notes and a low, or any other of the 
combinations of the preceding table, and he cannot 
fail to be convinced there is in each case a charac- 
teristic sound, which needs no musical ear for its 


appreciation, and which cannot be misunderstood 
by any one who has heard it, or has read it as the 
description of the sound of such and such a light- 
house, or has been told of it by word of mouth. 
The distinction between long and short blasts, as 
Mr. Price Edwards pointed out in his communication 
to the Society of Arts already referred to, has not 
proved satisfactory in experience ; and I believe 
this will generally be admitted to be the case by 
those who have experience of the working of the 
Morse system of long and short blasts of the steam 
whistle or siren at sea. There is an uncertainty 
as to the instant when the sound ceases, prolonged 
as it often is by echoes, and in the case of the 
steam whistle an uncertainty also as to when it 
begins, which is very distressing to any one trying 
to understand Morse signals by -long and short 
sounds. But corresponding signals by very short 
high and low notes following one another very 
quickly, with ample times of silence between the 
groups of sounds, are exceedingly clear and may 
easily be distinguished, even when the sounds are 
barely audible. 


[Address delivered before the Royal Society of Edinburgh, 
December iZth, 1865.] 

THE forces concerned in the laying arid lifting 
of deep submarine cables attracted much public 
attention in the years 1857-58. 

An experimental trip to the Bay of Biscay in May 
1858, proved the possibility, not only of safely 
laying such a rope as the old Atlantic cable in very 
deep water, but of lifting it from the bottom with- 
out fracture. The speaker had witnessed the almost 
incredible feat of lifting up a considerable length 
of that slight and seemingly fragile thread from a 
depth of nearly 2\ nautical miles. 1 The cable had 

1 Throughout the following statements, the word mile will be 
used to denote (not that most meaningless of modern measures, the 
British statute mile) but the nautical mile, or the length of a minute 
of latitude, in mean latitudes, which is 6,073 feet. For approximate 
statements, rough estimates, &c., it may be taken as 6,000 feet, or 
1,000 fathoms. 


. , __ 

actually brought with it safely to the surface, from 
the bottom, a splice with a large weighted frame 
attached to it, to prevent untwisting between the 
two ships, from which two portions of cable with 
opposite twists had been laid. The actual laying of 
the cable a few months later, from mid ocean to 
Valencia on one side, and Trinity Bay, Newfound- 
land, on the other, regarded merely as a mechanical 
achievement, took by surprise some of the most 
celebrated engineers of the day, who had not 
concealed their opinion, that the Atlantic Telegraph 
Company had undertaken an impossible problem. 
As a mechanical achievement it was completely 
successful ; and the electric failure, after several 
hundred messages (comprising upwards of 4,359 
words) had been transmitted between Valencia and 
Xewfoundland, was owing to electric faults existing 
in the cable before it went to sea. Such faults 
cannot escape detection, in the course of the 
manufacture, under the improved electric testing 
since brought into practice, and the causes which 
led to the failure of the first Atlantic cable no 
longer exist as dangers in submarine telegraphic 


enterprise. But the possibility of damage being- 
done to the insulation of the electric conductor 
before it leaves the ship (illustrated by the occur- 
rences which led to the temporary loss of the 1865 
cable), implies a danger which can only be 
thoroughly guarded against by being ready at any 
moment to back the ship and check the egress of 
the cable, and to hold on for some time, or to haul 
back some length according to the results of 
electric testing. 

The forces concerned in these operations, and the 
mechanical arrangements by which they are 
applied and directed, constitute one chief part of 
the present address ; the remainder is devoted to 
explanations as to the problem of lifting the west 
end of the 1,200 miles of cable laid last summer, 
from Valencia westwards, and now lying in perfect 
electric condition (in the very safest place in which 
a submarine cable can be kept), and ready to do its 
work, as soon as it is connected with Newfoundland, 
by the 600 miles required to complete the line. 


Forces concerned in the Submergence of a Cable. 

In a paper published in the Engineer Journal 
in 1857, the speaker had given the differential 
equations of the catenary formed by a submarine 
cable between the ship and the bottom, during the 
submergence, under the influence of gravity and 
fluid friction and pressure ; and he had pointed out 
that the curve becomes a straight line in the case 
of no tension at the bottom. As this is always the 
case in deep-sea cable laying, he made no farther 
reference to the general problem in the present 

When a cable is laid at uniform speed, on a level 
bottom, quite straight, but without tension, it forms 
an inclined straight line, from the point where it 
enters the water, to the bottom, and each point of 
it clearly moves uniformly in a straight line towards 
the position on the bottom that it ultimately 
occupies. 1 That is to say, each particle of the 
cable moves uniformly along the base of an isosceles 

1 Precisely the movement of a battalion in line changing front. 


triangle, of which the two equal sides are the 
inclined portion of the cable between it and the 
bottom, and the line along the bottom which this 
portion of the cable covers when laid. When the 
cable is paid out from the ship at a rate exceeding 
that of the ship's progress, the velocity and direc- 
tion of the motion of any particle of it through the 
water are to be found by compounding a velocity 
along the inclined side, equal to this excess, with 
the velocity already determined, along the base of 
the isosceles triangle. 

The angle between the equal sides of the isos- 
celes triangle, that is to say, the inclination which 
the cable takes in the water, is determined by the 
condition, that the transverse component of the 
cable's weight in water is equal to the transverse 
component of the resistance of the water to its 
motion. Its tension where it enters the water is 
equal to the longitudinal component of the weight 
(or, which is the same, the whole weight of a length 
of cable hanging vertically down to the bottom), 
diminished by the longitudinal component of the 
fluid resistance. In the laying of the Atlantic 


cable, when the depth was two miles, the rate of 
the ship six miles an hour, and the rate of paying 
out of the cable, seven miles an hour, the resistance 
to the egress of the cable accurately measured by a 
dynamometer, was only 14 cwt. But it must have 
been as much as 28 cwt., or the weight of two miles 
of the cable hanging vertically down in water, were 
it not for the frictional resistance of the water against 
the cable slipping, as it were, down an inclined 
plane from the ship to the bottom, which therefore 
must have borne the difference, or 14 cwt. Accurate 
observations are wanting as to the angle at which 
the cable entered the water ; but from measure- 
ments of angles at the stern of the ship, and a 
dynamical estimate (from the measured strain) of 
what the curvature must have been between the 
ship and the water, I find that its inclination in the 
water, when the ship's speed was nearly 6J miles 
per hour, must have been about 6j, that is to say, 
the incline was about I in 8^. Thus the length of 
cable, from the ship to the bottom, when the water 
was 2 miles deep, must have been about 17 miles. 
The whole amount (14 cwt.) of fluid resistance to 


the motion of this length of cable through it, is 
therefore about '81 of a cwt. per mile. The longi- 
tudinal component velocity of the cable through 
the water, to which this resistance was due, may be 
taken, with but very small error, as simply the 
excess of the speed of paying out above the 
speed of the ship, or about I mile an hour. Hence, 
to haul up a piece of the cable vertically through the 
water, at the rate of I mile an hour, would require 
less than I cwt. for overcoming fluid friction, per 
mile length of the cable, over and above its weight 
in water. Thus fluid friction, which for the laying 
of a cable performs so valuable a part in easing the 
strain with which it is paid out, offers no serious 
obstruction, indeed, scarcely any sensible obstruc- 
tion, to the reverse process of hauling back, if done 
at only I mile an hour, or any slower speed. 

As to the transverse component of the fluid 
friction, it is to be remarked that, although not 
directly assisting to reduce the egress strain, it 
indirectly contributes to this result; for it is the 
transverse friction that causes the gentleness of the 
slope, giving the sufficient length of 17 miles of 


cable slipping down through the water, on which 
the longitudinal friction operates, to reduce the 
egress strain to the very safe limit formed in the 
recent expedition. In estimating its amount, even 
if the slope were as much as I in 5, we should 
commit only an insignificant error, if we supposed 
it to be simply equal to the weight of the cable in 
water, or about 14 cwt. per mile for the 1865 
Atlantic cable. The transverse component velocity 
to which this is due may be estimated with but 
insignificant error, by taking it as the velocity of a 
body moving directly to the bottom in the time 
occupied in laying a length of cable equal to the 17 
miles of oblique line from the ship to the bottom. 
Therefore, it must have been about 2 miles in 
17 -v- 6J = 2*6 1 hours, or *8 of a mile per hour. It is 
not probable that the actual motion of the cable 
lengthwise through the water can affect this result 
much. Thus, the velocity of settling of a horizontal 
piece of the cable (or velocity of sinking through 
the water, with weight, just borne by fluid friction) 
would appear to be about '8 of a mile per hour. 
This may be contrasted with longitudinal friction 


by remembering that, according to the previous 
result, a longitudinal motion through the water at 
the rate of I mile per hour is resisted by only T Vth 
of the weight of the portion of cable so moving. 

These conclusions justify remarkably the choice 
that was made of materials and dimensions for the 
1865 cable. A more compact cable (one for 
instance with less gutta percha, less or no tow 
round the iron wires, and somewhat more iron), 
even if of equal strength and equal weight per mile 
in water, would have experienced less transverse 
resistance to motion through the water, and there- 
fore would have run down a much steeper slope 
to the bottom. Thus, even with the same longi- 
tudinal friction per mile, it would have been less 
resisted on .the shorter length ; but even on the 
same length it would have experienced much less 
longitudinal friction, because of its smaller circum- 
ference. Also, it is important to remark that the 
roughness of the outer tow covering undoubtedly 
did very much to ease the egress strain, as it must 
have increased the fluid friction greatly beyond 
what would have acted on a smooth gutta percha 


surface of or even on the surface smooth iron wires, 
presented by the more common form of submarine 

The speaker showed models illustrating the 
paying-out machines used on the Atlantic expe- 
ditions of 1858 and 1865. He stated that nothing 
could well be imagined more perfect than the 
action of the machine of 1865 in paying out the 
1,200 miles of cable then laid, and that if it were 
only to be used for paying out, no change either in 
general plan or in detail seemed desirable, except 
the substitution of a softer material for the "jockey 
pulleys," by which the cable in entering the 
machine has the small amount of resistance applied 
to it which it requires to keep it from slipping 
round the main drum. The rate of egress of the 
cable was kept always under perfect control by a 
weighted friction brake of Appold's construction 
(which had proved its good quality in the 1858 
Atlantic expedition) applied to a second drum 
carried on the same shaft with the main drum. 
When the weights were removed from the brake 
(which could be done almost instantaneously by 


means of a simple mechanism), the resistance to 
the egress of the cable, produced by "jockey 
pulleys," and the friction at the bearings of the 
shaft carrying the main drum, &c., was about 2 

Procedure to Repair the Cable in case of the appear- 
ance of an electric fault diiring the laying. 

In the event of a fault being indicated by the 
electric test at any time during the paying out, the 
safe and proper course to be followed in future (as 
proved by the recent experience), if the cable is of 
the same construction as the present Atlantic cable, 
is instantly, on order given from an authorised 
officer in the electric room, to stop and reverse the 
ship's engines, and to put on the greatest safe 
weight on the paying-out brake. Thus in the 
course of a very short time the egress of the cable 
may be stopped, and if the weather is moderate, 
the ship may be kept, by proper use of paddles, 
screw, and rudder, nearly enough in the proper 
position for hours to allow the cable to hang down 
almost vertically, with little more strain than the 


weight of the length of it between the ship and 
the bottom. 

The best electric testing that has been practised 
or even planned cannot show within a mile the 
position of a fault consisting of a slight loss of 
insulation, unless both ends of the cable are at hand. 
Whatever its character may be, unless the electric 
tests demonstrate its position to be remote from 
the outgoing part, the only thing that can be done 
to find whether it is just on board or just overboard, 
is to cut the cable as near the outgoing part as the 
mechanical circumstances allow to be safely done. 
The electric test immediately transferred to the 
fresh-cut seaward end shows instantly if the line is 
perfect between it and the shore. A few minutes 
more, and the electric tests applied to the two ends 
of the remainder on board, will, in skilful hands, 
with a proper plan of working, show very closely 
the position of the fault whatever its character may 
be. The engineers will thus immediately be able 
to make proper arrangements for resplicing and 
paying out good cable, and for cutting out the fault 
from the bad part. 

VOL. in. F F 


But if the fault is between the land end and 
the fresh-cut seaward end on board ship, 
proper simultaneous electric tests on board 
ship and on shore (not hitherto practised, but 
easy and sure if properly planned) must be used 
to discover whether the fault lies so near the ship 
that the right thing is to haul back the cable 
until it is got on board. If it is so, then steam 
power must be applied to reverse the paying- 
out machine, and, by careful watching of the 
dynamometer, and controlling the power accord- 
ingly (hauling in slowly, stopping, or veering out a 
little, but never letting the dynamometer go above 
60 or 65 cwt.), the cable (which can bear 7 tons) 
will not break, and the fault will be got on board 
more surely, and possibly sooner, than a " sulky " 
salmon of 30 Ibs. can be landed by an expert 
angler with a line and rod that could .not bear 
10 Ibs. The speaker remarked that he was entitled 
to make such assertions with confidence now 
because the experience of the late expedition had 
not only verified the estimates of the scientific 
committee and of the contractors as to the strength 


of the cable, its weight in water (whether deep or 
shallow), and its mechanical manageability, but it 
had proved that in moderate weather the Great 
Eastern could, by skilful seamanship, be kept in 
position and moved in the manner required. She 
had actually been so for thirty-eight hours, and 
eighteen hours during the operations involved in 
the hauling back and cutting out the first and 
second faults and reuniting the cable, and during 
seven hours of hauling in, in the attempt to 
repair the third fault. 

Should the simultaneous electric testing on board 
and on shore prove the fault to be 50 or 100 or 
more miles from the ship, it would depend on the 
character of the fault, the season of the year, and 
the means and appliances on board, whether it 
would be better to complete the line, and after- 
wards, if necessary, cut out the fault and repair, or 
to go back at once and cut out the fault before 
attempting to complete the line. Even the worst 
of these contingencies would not be fatal to the 
undertaking w<ith such a cable as the present one. 
But all experience of cable-laying shows that 

F F 2 


almost certainly the fault would either be found on 
board, or but a very short distance overboard, and 
would be reached and cut out with scarcely any 
risk, if really prompt measures, as above described, 
are taken at the instant of the appearance of a 
fault, to stop as soon as possible with safety the 
further egress of the cable. 

The most striking part of the Atlantic under- 
taking proposed for 1866, is that by which the 
1,200 miles of excellent cable laid in 1865 is to be 
utilised by completing the line to Newfoundland. 

That a cable lying on the bottom in water two 
miles deep can be caught by a grapnel and raised 
several hundred fathoms above the bottom, was 
amply proved by the eight days' work which 
followed the breakage of the cable on the 3rd of 
August last. Three times out of four that the 
grapnel was let down, it caught the cable, on each 
occasion after a few hours of dragging, and with 
only 300 or 400 fathoms more of rope than the 
2,100 required to reach the bottom by the shortest 
course. The time when the grapnel did not 
hook the cable it came up with one of its flukes 


caught round by its chain ; and the grapnel, the 
short length of chain next it, and about 200 
fathoms of the wire rope, were proved to have been 
dragged along the bottom, by being found when 
brought on board to have interstices filled with 
soft light gray ooze (of which the speaker showed 
a specimen to the Royal Society). These results 
are quite in accordance with the dynamical theory 
indicated above (see Appendix II.), according to 
which a length of such rope as the electric cable, 
hanging down with no weight at its lower end, and 
held by a ship moving through the water at half a 
mile an hour, would slope down to the bottom at 
an angle from the vertical of only 22 ; and the 
much heavier and denser wire-rope that was used 
for the grappling would go down at the same angle 
with a considerably more rapid motion of the 
ship, or at a much steeper slope with the same 
rate of motion of the ship. 

The only remaining question is : How is the 
cable to be brought to the surface when hooked ? 
The operations of last August failed from the 
available rope, tackle, and hauling machine not 


being strong enough for this very unexpected 
work. On no occasion was the electric cable 
broken. 1 With strong enough tackle, and a 
hauling machine, both strong enough, and under 
perfect control, the lifting of a submarine cable, as 
good in mechanical quality as the Atlantic cable 
of 1865, by a grapnel or grapnels, from the bottom 
at a depth of two miles, is certainly practicable. If 
one attempt fails, another will succeed ; and there 
is every reason, from dynamics as well as from the 
1865 experience, to believe that in any moderate 
weather the feat is to be accomplished with little 
delay, and with very few if any failing attempts. 

1 The strongest rope available was a quantity of rope of iron 
wire and hemp spun together, able to bear fourteen tons, which was 
prepared merely as buoy-rope (to provide for the contingency of 
being obliged, by stress of weather or other cause, to cut and leave 
the cable in deep or shallow water), and was accordingly all in 
100 fathoms-lengths, joined by shackles with swivels. The wire 
and hemp rope itself never broke, but on two of the three occasions 
a swivel gave way. On the last occasion, about 900 fathoms of 
Manilla rope had to be used for the upper part, there not being 
enough of the wire buoy-rope left ; and when 700 fathoms of it had 
been got in, it broke on board beside a shackle, and the remaining 
200 fathoms of the Manilla, with 1,540 fathoms of wire-rope and 
the grapnel, and the electric cable which it had hooked, were all 
lost for the year 1865. 


The several plans of proceeding that have been 
proposed are of two classes those in which, by 
three or more ships, it is proposed to bring a point 
of the cable to the surface without breaking it at 
all ; and those in which it is to be cut or broken, 
and a point of the cable somewhat eastward from 
the break is to be brought to the surface. 

With reference to either class, it is to be 
remarked that, by lifting simultaneously by several 
grapnels so constructed as to hold the cable 
without slipping along it or cutting it, it is possible 
to bring a point of the cable to the surface without 
subjecting it to any strain amounting to the weight 
of a length of cable equal to the depth of the 

The plan which seemed to the speaker surest 
and simplest is to cut the cable at any chosen 
point, far enough eastward of the present broken 
end to be clear of entanglement of lost buoy-rope, 
grapnels, and the loose end of the electric cable 
itself; and then, or as soon as possible after, to 
grapple and lift at a point about three miles farther 
eastward. This could be well and safely done by 


two ships, one of them with a cutting grapnel, and 
the other (the Great Eastern herself) with a holding 
grapnel. This plan was illustrated by lifting, by 
aid of two grapnels, a very fragile chain (a common 
brass chain in short lengths, joined by links of fine 
cotton thread) from the floor of the Royal Society. 
It was also pointed out that it can be executed by 
one ship alone, with only a little delay, but with 
scarcely any risk of failure. Thus, by first hooking 
the cable by a holding grapnel, and hauling it up 
200 or 300 fathoms from the bottom, it may be 
left there hanging by the grapnel-rope on a buoy, 
while the ship proceeds three miles westwards, cuts 
the cable there, and returns to the buoy. Then, it 
is an easy matter, in any moderate weather, to 
haul up safely and get the cable on board. 

The use of the dynamometer in dredging was 
explained ; and the forces operating on the ship, 
the conditions of weather, and the means of 
keeping the ship in proper position during the 
process of slowly hauling in a cable, even if it were 
of strength quite insufficient to act, when nearly 
vertical, with any sensible force on the ship, were 


discussed at some length. The manageability of 
the Great Eastern, in skilful hands, had been 
proved by Captain Anderson (now Sir James 
Anderson) to be very much better than could have 
been expected, and to be sufficient for the require- 
ments in moderate weather. She has both screw 
and paddles an advantage possessed by no other 
steamer in existence. By driving the screw at full 
power ahead, and backing the paddles to prevent the 
ship from moving ahead, or (should the screw over- 
power the paddles), by driving the paddles full power 
astern, and driving at the same time the screw ahead 
with power enough to prevent the ship from going 
astern, " steerage way " is created by the lash of 
water from the screw against the rudder ; and thus 
the Great Eastern may be effectually steered with- 
out going ahead. Thus she is, in calm or moderate 
weather, almost as' manageable as a small tug 
steamer with reversing paddles, or as a rowing boat. 
She can be made still more manageable than 
she proved to be in 1865, by arranging to disconnect 
either paddle at any moment ; which, the speaker 
was informed by Mr. Canning, may easily be done. 


The speaker referred to a letter he had received 
from Mr. Canning, chief engineer of the Telegraph 
Construction and Maintenance Company, inform- 
ing him that it is intended to use three ships, and 
to be provided both with cutting and with holding 
grapnels, and expressing great confidence as to the 
success of the attempt. In this confidence the 
speaker believed every practical man who witnessed 
the Atlantic operations of 1865 shared, as did also, 
to his knowledge, other engineers who were not 
present on that expedition, but who were well 
acquainted with the practice of cable laying and 
mending in various seas, especially in the Medi- 
terranean. The more he thought of it himself, 
both from what he had witnessed on board the 
Great Eastern, and from attempts to estimate on 
dynamical principles the forces concerned, the 
more confident he felt that the contractors would 
succeed next summer in utilising the cable partly 
laid in 1865, and completing it into an electrically 
perfect telegraphic line between Valencia and 



1858 AND 1865. 

(Distance from Ireland to Newfoundland, 1,670 Nautical Miles.) 

Old Atlantic Cable, 1858. 

Conductor. A copper strand, consisting of seven 
wires (six laid round one), and weighing 107 Ibs. 
per nautical mile. 

Insulator. Gvtta percha laid on in three 
coverings, and weighing 261 Ibs. per knot. 

External Protection. Eighteen strands of char- 
coal iron wire, each strand composed of seven wires 
(six laid round one), laid spirally round the core, 
which latter was previously padded with a serving 
of hemp saturated with a tar mixture. The 
separate wires were each 22 gauge ; the stand 
complete was No. 14 gauge. 

Circumference of Finished Cable y 2 inches. 

Weight in Air, 20 cwt. per nautical mile. 

WeigJit in Water, I3'4 cwt. per nautical mile. 

Breaking Strain, 3 tons 5 cwt., or equal to 4-85 
times the cable's weight in water per mile. Hence 
the cable would bear its own weight in nearly five 
miles depth of water, or 2*05 times the 


Deepest Water to be encountered, 2,400 fathoms, 
being less than 2\ nautical miles. 

Length of Cable Shipped, 2,174 nautical miles. 

New Atlantic Cable, 1865. 

Conductor. Copper strand consisting of seven 
wires (six laid round one), and weighing 300 Ibs. 
per nautical mile, embedded for solidity in Chatter- 
ton's compound. Diameter of single wire -048 = 
ordinary No. 18 gauge. Gauge of strand '144 = 
ordinary No. 10 gauge. 

Insulation. Gutta percha, four layers of which 
are laid on alternately with four thin layers of 
Chatterton's compound. The weight of the entire 
insulation 400 Ibs. per nautical mile. Diameter of 
core '464 of an inch; circumference of core 1*46 

External Protection. Ten solid wires of diameter 
095 (No. 13 gauge) drawn from Webster and 
Horsfall's homogeneous iron, each wire surrounded 
separately with five strands of Manilla yarn, 
saturated with a preservative compound, and the 
whole laid spirally round the core, which latter is 
padded with ordinary hemp, saturated with pre- 
servative mixture. 

Circumference of Finished Cable, 3*534 inches. 

Weight in Air, 35 cwt. 3 qrs. per nautical mile. 
Weight in Water, 14 cwt, per nautical mile. 

Breaking Strain, 7 tons 1 5 cwt, or equal to eleven 


times the cable's weight in water per mile. Hence, 
the cable will bear its own weight in eleven miles 
depth of water, or 4*64 times the 

Deepest Water to be encountered, 2,400 fathoms, 
or less than 2\ nautical miles. 

Length of Cable Shipped, 2,300 nautical miles. 


Let W be the weight of the cable per unit of its 
length in water ; T the force with which the cable 
is held back at the point where it reaches the 
water (which may be practically regarded as equal 
to the force with which its egress from the ship is 
resisted by the paying-out machinery, the differ- 
ence amounting only to the weight in air of a piece 
of cable equal in length to the height of the stern 
pulley above the water) ; P and Q the transverse 
and longitudinal components of the force of 
frictional resistance experienced by the cable in 
passing through the water from surface to bottom ; 
i the inclination of its line to the horizon ; D the 
depth of the water. 

The whole length of cable from surface to 

bottom will be - ; and the transverse and 
sin i 

longitudinal components of the weight of this 

portion are therefore - - cos 2, and WD respec- 
sin t 


tively. These are balanced by 

P and T + Q -5- 

sin i sin i 


P = W cos *, Q =(w -5) sin i. . . . (i.) 

To find the corresponding components of the 
velocity of the cable through the water, which we 
shall denote by/ and q, we have only to remark 
that the actual velocity of any portion of the cable 
in the water may be regarded as the resultant of 
two velocities, one equal and parallel to that of 
the ship forwards, and the other obliquely down- 
wards along the line of the cable, equal to that of 
the paying out, obliquely downwards along the 
line of the cable (since if the cable were not paid out, 
but simply dragged, while by any means kept in a 
straight line at any constant inclination, its motion 
would be simply that of the ship). Hence, if v be 
the ship's velocity, and u the velocity at which the 
cable is paid out from the ship, we have 

/ = v sin z, q u v cos *.,.... (2.) 

Now, as probably an approximate, and therefore 
practically useful, hypothesis, we may suppose 
each component of fluid friction to depend solely 
on the corresponding component of the fluid 
velocity, and to be proportional to its square. 
Thus we may take 

P-W, Q = W . . . .(3.) 


where p and q denote the velocities, transverse and 
longitudinal, which would give frictions amounting 
to the weight of the cable ; or, as we may call them 
the transverse and longitudinal settling velocities. 
We may use these equations merely as introducing 
a convenient piece of notation for the components 
of fluid friction, without assuming any hypothesis, 
if we regard p and as each some unknown 
function of/ and q. It is probable that p depends 
to some degree on q, although chiefly on p ; and 
vice versa, q to some degree on /, but chiefly on q. 
It is almost certain, however, from experiments 
such as those described in Beaufoy's Nautical 
Experiments, that p and q are each very nearly 
constant for all practical velocities. 

Eliminating/ and q between (i), (2), and (3), we 

which gives 

v sin i 


(WD - T) sin i = WD 
which gives 

These formulae apply to every case of uniform 
towing of a rope under water, or hauling in, or 
paying out, whether the lower end reaches the 
bottom or not, provided always the lower end is 


free from tension ; but if it is not on the bottom, D 
must denote its vertical depth at any moment, 
instead of the whole depth of the sea. To apply 
to the case of merely towing, we must put u = o ; 
or, to apply to hauling in, we must suppose u 

It is to be remarked that the inclination assumed 
by the cable under water does not depend on its 
longitudinal slip through the water (since we 
assume this not to influence the transverse com- 
ponent of fluid friction), and that, according to 
equation (4), it is simply determined by the ratio 
of the ship's speed to the transverse " settling 
velocity" of the cable. 

The following table shows the ratio of the ship's 
speed to the " transverse settling velocity " of the 
cable for various degrees of inclination of the cable 
to the horizon : 

Ratio of Ship's 

Ratio of Ship's 

of Cable 

Speed to 
" transverse 

of Cable 

Speed to 
" transverse 

to Horizon. 

settling velocity' ' 
of Cable. 

to Horizon. 

settling z>elocity ' 
of Cable. 

v *J cos i 

v *J cos i 


p sin i 


p sin i 





angle \ 
whose sine \ t . - 

. T ( I- 5 


5 o , 

51 50 

I -0466 


1S 7 ' 





















i '5779 






If the inclination of the cable had been exactly 
6 45' when the speed of the Great Eastern was 
exactly 6\ miles per hour, the value of p for the 
Atlantic cable of 1865 would be exactly 6| -7-8*478, 
or 765 of a mile per hour. 



[Lecture delivered at the Conversazione of the Institution of 
Mechanical Engineers in the Science and Art Museum, 
Edinburgh, on Wednesday evening, yd August, 1887.] 

" WAVES " is a very comprehensive word. It 
comprehends waves of water, waves of light, waves 
of sound, and waves of solid matter such as are 
experienced in earthquakes. It also comprehends 
much more than these. " Waves " may be de- 
fined generally as a progression through matter of 
a state of motion. The distinction between the 
progress of matter from one place to another, and 
the progress of a wave from one place to another 
through matter, is well illustrated by the very 
largest examples of waves that we have largest 
in one dimension, smallest in another waves of 
light, waves which extend from the remotest star, 


at least a million times as far from us as the sun is. 
Think of ninety-three million million miles, and 
think of waves of light coming from stars known 
to be at as great a distance as that ! So much for 
the distance of propagation or progression of waves 
of light. But there are two other magnitudes con- 
cerned in waves : there is the wave-length and 
there is the amount of displacement of a moving 
particle in the wave. Waves of light consist of 
vibrations to and fro, perpendicular to the line of 
progression of the wave. The length of the wave 
I shall explain the meaning of "wave-length" 
presently : it speaks for itself in fact, if we look at 
waves of water the length from crest to crest in 
waves of light is from one thirty-thousandth to one 
fifty-thousandth or one sixty-thousandth of an inch ; 
and these waves of light travel through all known 
space. Waves of sound differ from waves of light 
in the vibration of the moving particles being 
along the line of propagation of the wave, instead 
of perpendicular to it. Waves of water agree more 
nearly with waves of light than do waves of sound ; 
but waves of water have this great distinction from 

G G 2 


waves of light and waves of sound, that they are 
manifested at the surface or termination of the 
medium or substance whose motion constitutes the 
wave. It is with waves of water that we are con- 
cerned to-night ; and of all the beautiful forms of 
water waves that of Ship Waves is perhaps the 
most beautiful, if we can compare the beauty of 
such beautiful things. The subject of ship waves 
is certainly one of the most interesting in mathe- 
matical science. It possesses a special and in- 
tense interest, partly from the difficulty of the 
problem, and partly from the peculiar com- 
plexity of the circumstances concerned in the 
configuration of the waves. 

Canal Waves. I shall not at first speak of 
that beautiful configuration or wave-pattern, which 
I am going to describe a little later, seen in the 
wake of a ship travelling through the open water 
at sea ; but I shall as included in my special 
subject of ship waves, refer in the first place to 
waves in a canal, and to Scott Russell's splendid 
researches on that subject, made about the year 
1834 fifty-three years ago and communicated 


by him to the Royal Society of Edinburgh. I 
gave a very general and abstract definition of 
the term " wave," let us now have it in the 
concrete : a wave of water produced by a boat 
dragged along a canal. In one of Scott Russell's 
pictures illustrating some of his celebrated ex- 
periments, is shown a boat in the position that 
he called behind the wave ; and in the rear of 
the boat is seen a procession of waves. It is 
this procession of waves that we have to deal 
with in the first place. We must learn to under- 
stand the procession of waves in the rear of the 
canal boat, before we can follow, or take up the 
elements of, the more complicated pattern which 
is seen in the wake of a ship travelling through 
open water at sea. Scott Russell made a fine 
discovery in the course of those experiments. 
He found that it is only when the speed of the 
boat is less than a certain limit that it leaves 
that procession of waves in its rear. Now 
the question that I am going to ask is, how 
is that procession kept in motion ? Does it 
take power to drag the boat along, and to 


produce or to maintain that procession of waves ? 
We all know it does take power to drag a boat 
through a canal ; but we do not always think 
on what part of the phenomena manifested by 
the progress of the boat through the canal, the 
power required to drag the boat depends. 

I shall ask you for a time to think of water 
not as it is, but as we can conceive a substance 
to be that is, absolutely fluid. In reality 
water is not perfectly fluid, because it resists 
change of shape ; and non-resistance to change 
of shape is the definition of a perfect fluid. 
Is water then a fluid at all ? It is a fluid 
because it permits change of shape; it is a fluid 
in the same sense that thick oil or treacle is a 
fluid. Is it only in the same sense ? I say 
yes. Water is no more fluid in the abstract 
than is treacle or thick oil. Water, oil, and 
treacle, all resist change of shape. When we 
attempt to make the change very rapidly, 
there is a great resistance; but if we make the 
change very slowly, there is a small resistance. 
The resistance of these fluids to change of 


shape is proportionate to the speed of the 
change : the quicker you change the shape, the 
greater is the force that is required to make 
the change. Only give it time, and treacle 
or oil will settle to its level in a glass or basin 
just as water does. No deviation from perfect 
fluidity, if the question of time does not enter, 
has ever been discovered in any of these fluids. 
In the case of all ordinary liquids, anything that 
looks like liquid and is transparent or clear 
or, even if it is not transparent, anything that 
is common^ called a fluid or liquid is per- 
fectly liquid in the sense of exerting no per- 
manent resistance to change of shape. The 
difference between water and a viscous substance, 
like treacle or oil, is defined merely by taking 
into account time. Now for some motions of 
water (as capillary waves), resistance to change 
of shape, or as we call it viscosity, has a very 
notable effect ; for other cases viscosity has no 
sensible effect. I may tell you this I cannot 
now prove it, for my function this evening is 
only to explain and bring before you generally 


some results of mathematical calculation and 
experimental observation on these subjects 
I may tell you that great waves at sea will 
travel for hours or even for days, showing 
scarcely any loss of sensible motion or of 
energy, if you will allow me so to call it 
through viscosity. On the other hand, look at 
the ripples in a little pond, or in a little pool 
of fresh rain water lying in the street, which are 
excited by a puff of wind ; the puff of wind is 
no sooner gone than the ripples begin to subside, 
and before you can count five or six the water 
is again perfectly still. The forces concerned in 
short waves such as ripples, and the forces 
concerned in long waves such as great ocean 
waves, are so related to time and to speed that, 
whereas in the case of short waves the viscosity 
which exists in water comes to be very potent, in 
the case of long waves it has but little effect. 

Allow me then for a short time to treat 
water as if it were absolutely free from vis- 
cosity as if it were a perfect fluid ; and I shall 
afterwards endeavour to point out where vis- 


cosity comes into play, and causes the results of 
observation to differ more or less very greatly 
in some cases, and very slightly in others 
from what we should calculate on the sup- 
position of water being a perfect fluid. If 
water were a perfect fluid, the velocity of pro- 
gression of a wave in a canal would be smaller 
the shorter the wave. That of a " long wave " 
whose length from crest to crest is many 
times the depth of the canal is equal to the 
velocity which a body acquires in falling from 
a height equal to half the depth of the canal. 
For brevity we might call this height the " speed- 
height" the height from which a body must 
fall to acquire a certain speed. The velocity in 
feet per second is approximately eight times 
the square root of the height in feet. Examples : 
a body falls from a height of 16 feet, and it 
acquires a velocity of 32 feet per second; a 
body falls from a height of 4 feet, the velo- 
city is only 16 feet per second; and so on. 
Thus in a canal 8 feet deep the natural velocity 
of the "long wave" is 16 feet per second, or 


about ii miles per hour. If water were a per- 
fect fluid, this would be the state of the case : 
a boat dragged along a canal at any velocity 
less than the natural speed of the long wave 
in the canal would leave a train of waves behind 
it of so much shorter length that their velocity 
of propagation would be equal to the velocity of 
the boat; and it is mathematically proved that 
the boat would take such a position as is shown 
in Scott Russell's diagram referred to, namely 
just on the rear slope of the wave. It was not 
by mathematicians that this was found out ; but 
it was Scott Russell's accurate observation and 
well devised experiments that first gave us these 
beautiful conclusions. 

To go back : a wave is the progression through 
matter of a state of motion. The motion cannot 
take place without the displacement of particles. 
Vary the definition by saying that a wave is the 
progression of displacement. Look at a field of 
corn on a windy day. You see that there is 
something travelling over it. That something is 
not the ears of corn carried from one side of the 


field to the other, but is the change of colour 
due to your seeing the sides or lower ends of 
the ears of corn instead of the tops. A laying 
down of the stalks is the thing that travels in 
the wave passing over the corn field. The thing 
that travels in the w r ave behind the boat is an 
elevation of the water at the crest and a depres- 
sion in the hollow. You might make a wave 
thus. Place over the surface of the water in 
a canal a wave-form, made from a piece of paste- 
board or of plastic material such as gutta-percha 
that you can mould to any given shape; and 
take care that the water fills up the wave-form 
everywhere, leaving no bubbles of air in the 
upper bends. Now you have a constant dis- 
placement of the water from its level. Now take 
your gutta-percha form and cause it to move 
along drag it along the surface of the 
canal and you will thereby produce a wave. 
That is one of the best and most convenient of 
mathematical ways of viewing a wave. Imagine 
a wave generated in that way ; calculate what 
kind of motion can be so generated, and you have 


not merely the surface motion produced by the 
force that you applied, but you have the water- 
motion in the interior. You have the whole 
essence of the thing discovered, if you can 
mathematically calculate from a given motion 
at the surface what is the motion that necessarily 
follows throughout the interior ; and that can 
be done, and is a part of the elements of the 
mathematical results which I have to bring 
before you. 

Now to find mathematically the velocity of 
progression of a free wave, proceed thus. Take 
your gutta-percha form and hold it stationary 
on the surface of the water ; the water-pressure 
is less at the crest and greater at the hollow ; 
by the law of hydrostatics, the deeper down you 
go, the greater is the pressure. Move your form 
along very rapidly, and a certain result, a centri- 
fugal force, due to the inertia of the flowing 
water, will now cause the pressure to be greatest 
at the crest and least at the lowest point of the 
hollow. Move it along at exactly the proper 
speed and you will cause the pressure to be 


equal all over the surface of the gutta-percha 
form. Now have done with the gutta-percha. 
We only had in it imagination. Having imagined 
it and got what we wanted out of it, discard it. 
When moving it at exactly this proper speed, you 
have a free wave. That is a slight sketch of 
the mode by which we investigate mathemati- 
cally the velocity of the free wave. It was by 
observation that Scott Russell found it out ; and 
then there was a mathematical verification, not 
of the perfect theoretic kind, but of a kind 
which showed a wonderful grasp of mind and 
power of reasoning upon the phenomena that 
he had observed. 

But still the question occurs to everybody 
who thinks of these things in an engineering 
way, how does that procession require work to 
be done to keep it up ? or does it require work 
to be done at all ? May it not be that the work 
required to drag the boat along the canal has 
nothing to do with the waves after all ? that 
the formation of the procession of waves once 
effected leaves nothing more to be desired in 


the way of work ? that the procession once 
formed will go on of itself, requiring no work 
to sustain it ? Here is the explanation. The 
procession has an end. The canal may be 
infinitely long, the time the boat may be 
going may be as long as you please; but let 
us think of a beginning the boat started, the 
procession began to form. The next time you 
make a passage in a steamer, especially in smooth 
water, look behind the steamer, and you will 
see a wave or two as the steamer gets into motion. 
As it goes faster and faster, you will see a 
wave-pattern spread out; and if you were on 
shore, or in a boat in the wake of the steamer, 
you would see that the rear end of the procession 
of waves follows the steamer at an increasing 
distance behind. It is an exceedingly complicated 
phenomenon, and it would take a great deal of 
study to make out the law of it merely from 
observation. In a canal the thing is more simple. 
Scott Russell however did not include this in 
his work. This was left to Stokes, to Osborne 
Reynolds, and to Lord Rayleigh. The velocity 


of progress of a wave is one thing ; the velocity 
of the front of a procession of waves, and of 
the rear of a procession of waves, is another 
thing. Stokes made a grand new opening, show- 
ing us a vista previously unthought of in dynam- 
ical science. As was his manner, he did it 
merely in an examination question set for the 
candidates for the Smith prize in the University 
of Cambridge. I do not remember the year, 
and I do not know whether any particular candi- 
date answered the question ; but this I know, 
that about two years after the question was 
put, Osborne Reynolds answered it with very 
good effect indeed. In a contribution to the 
Plymouth Meeting of the British Association 
in 1877 (see Nature 23 Aug. 1877, pages 
343 4), in which he worked out one great 
branch at all events of the theory thus pointed 
out by Stokes, Reynolds gave this doctrine of 
energy that I am going to try to explain ; and 
a few years later Lord Rayleigh took it up and 
generalised it in the most admirable manner, 
laying the foundation not only of one part, but 


of the whole, of the theory of the velocity of 
groups of waves. 

The theory of the velocity of groups of waves, 
on which is founded the explanation of the 
wave-making resistance to ships whether in a 
canal or at sea, I think I have explained in 
such a way that I hope every one will 
understand the doctrine in respect to waves in 
a canal ; it is more complex in respect to waves 
at sea. I shall try to give you something on 
that part of the subject ; but as to the dynami- 
cal theory, you will see it clearly in regard to 
waves in a canal. If Scott Russell's drawing were 
continued backwards far enough, it would show 
an end to the procession of waves in the rear 
of the boat ; and the distance of that end would 
depend on the time the boat had been travelling. 
You will remember that we have hitherto been 
supposing water to be free from viscosity; but 
in reality water has enough of viscosity to 
cause the cessation of the wave procession at 
a distance corresponding to 50 or 60 or 100 
or 1000 wave-lengths in the rear of the ship. 


In a canal especially viscosity is very effective, 
because the water has to flow more or less across 
the bottom and up and down by the banks ; 
so that we have not there nearly the same freedom 
that we have at sea from the effects of viscosity 
in respect to waves. The rear of the procession 
travels forward at half the speed of the ship, 
if the water be very deep. What do I mean 
by very deep ? I mean a depth equal to 
at least one wave-length ; but it will be nearly 
the same for the waves if the depth be three- 
quarters of a wave-length. For my present pur- 
pose in which I am not giving results with 
minute accuracy, we will call very deep any depth 
more than three-quarters of the wave-length. 
For instance, if the depth of the water in the 
canal is anything more than three-quarters of 
the length from crest to crest of the waves, the 
rate of progression of the rear of the procession 
will be half the speed of the boat. Here then 
is the state of the case. The boat is followed by 
an ever-lengthening procession of waves; and 
the work required to drag the boat along in 


the canal supposing that the water is free from 
viscosity is just equal to the work required 
to generate the procession of waves lengthening 
backwards behind the boat at half the speed of 
the boat. The rear of the procession travels for- 
wards at half the speed of the boat ; the proces- 
sion lengthens backwards relatively to the boat at 
half the speed of the boat. There is the whole 
thing ; and if you only know how to calculate 
the energy of a procession of waves, assuming 
the water free from viscosity, you can calculate 
the work which must be done to keep a canal 
boat in motion. 

But now note this wonderful result : if the 

motion of the canal boat be more rapid than 

the most rapid possible wave in the canal 

(that is, the long wave), it cannot leave behind 

it a procession of waves it cannot make waves, 

properly so called, at all ; it can only make a 

hump or a hillock travelling with the boat, as 

shown in another of Scott Russell's drawings. 

What would you say of the work required to 

move the boat in that case ? You may answer 


that question at once : it would require no work ; 
start it, and it will go on for ever. Every one 
understands that a curling stone projected along 
the ice would go on for ever, were it not for the 
friction of the ice ; and therefore it must not 
seem so wonderful that a boat started moving 
through water would also go on for ever, if the 
water were perfectly fluid : it woiild not> if it is 
forming an ever-lengthening procession of waves 
behind it ; it would go on for ever, if it is not 
forming a procession of waves behind it. The 
answer then simply is, give the boat a velocity 
greater than the velocity of propagation of the 
most rapid wave (the long wave) that the canal 
can have ; and in these circumstances, ideal 
so far as nullity of viscosity is concerned, it 
will travel along and continue moving without 
any work being done upon it. I have said that 
the velocity of the long wave in a canal is equal 
to the velocity which a body acquires in falling 
from a height equal to half the depth of the 
canal. The term " long wave " I may now further 
explain as meaning a wave whose length is many 

H H 2 


times the depth of the water in the canal 50 
times the depth will fulfil this condition the 
length being always reckoned from crest to crest. 
Now if the wave-length from crest to crest be 50 
or more times the depth of the canal, then the 
velocity of the wave is that acquired by a body 
falling through a height equal to half the depth 
of the canal ; if the wave-length be less than that, 
the velocity can be expressed only by a complex 
mathematical formula. The results have been 
calculated ; but I need not put them before you, 
because we are not going to occupy ourselves 
with them. 

The conclusion then at which we have arrived is 
this : supposing at first the velocity of the boat to 
be such as to make the waves behind it of wave- 
length short in comparison with the depth of water 
in the canal : let the boat go a little faster, and 
give it time until steady waves are formed behind 
it ; these waves will be of longer wave-length : the 
greater the speed of the boat, the longer will be the 
wave-length, until we reach a certain limit ; and as 
the wave-length begins to be equal to the depth, 


or twice the depth, or three times the depth, we 
approach a wonderful and critical condition of 
affairs we approach the case of constant wave 
velocity. There will still be a procession of waves 
behind the boat, but it will be a shorter procession 
and of higher waves ; and this procession will not 
now lengthen astern at half the speed of the boat, 
but will lengthen perhaps at a third, or a fourth, or 
perhaps at a tenth of the .speed of the boat. We 
are approaching the critical condition : the rear of 
the procession of waves is going forward nearly as 
fast as the boat. This looks as if we were coming 
to a diminished resistance ; but it is not really so. 
Though the procession is lengthening less rapidly 
relatively to the boat than when the speed was 
smaller, the waves are very much higher ; and we 
approach almost in a tumultuous manner to a 
certain critical velocity. I will read you presently 
Scott Russell's words on the subject. Once that 
crisis has been reached, away the boat goes merrily, 
leaving no wave behind it, and experiencing no 
resistance whatever if the water be free from 
viscosity, but in reality experiencing a very large 


resistance, because now the viscosity of the water 
begins to tell largely on the phenomena. I think 
you will be interested in hearing Scott Russell's 
own statement of his discovery. I say his dis- 
covery, but in reality the discovery was made by a 
horse, as you will learn. I found almost surprisingly 
in a mathematical investigation, " On Stationary 
Waves in Flowing Water," contributed to the 
Philosophical Magazine (October, November, 
December, 1886, and January, 1887), a theoretical 
confirmation, forty-nine and a half years after 
date, of Scott Russell's brilliant "Experimental 
Researches into the Laws of Certain Hydrody- 
namical Phenomena that accompany the Motion 
of Floating Bodies, and have not previously been 
reduced into conformity with the known Laws of 
the Resistance of Fluids." * 

These experimental researches led to the 
Scottish system of fly-boats carrying passengers 
on the Glasgow and Ardrossan Canal, and between 

1 By John Scott Russell, Esq., M.A., F.R.S.E. Read before 
the Royal Society of Edinburgh, 3rd April, 1837, and published in 
the Transactions in 1840. 


Edinburgh and Glasgow on the Forth and Clyde 
Canal, at speeds of from eight to thirteen miles an 
hour, each boat drawn by a horse or pair of horses 
galloping along the bank. The method originated 
from the accident of a spirited horse, whose duty it 
was to drag the boat along at a slow walking 
speed, taking fright and running off, drawing the 
boat after him ; and it was discovered that, when 
the speed exceeded the velocity acquired by a 
body falling through a height equal to half the 
depth of the canal (and the horse certainly found 
this), the resistance was less than at lower speeds. 
Scott Russell's description of how Mr. Houston 
took advantage for his Company of the horse's 
discovery is so interesting that I quote it in 
extenso : 

" Canal navigation furnishes at once the most 
interesting ^illustrations of the interference of the 
wave, and most important opportunities for the 
application of its principles to an improved system 
of practice. 

"It is to the diminished anterior section of dis- 
placement, produced by raising a vessel with a 


sudden impulse to the summit of the progressive 
wave, that a very great improvement recently 
introduced into canal transports owes its existence. 
As far as I am able to learn, the isolated fact 
was discovered accidentally on the Glasgow and 
Ardrossan Canal of small dimensions. A spirited 
horse in the boat of William Houston, Esq., one of 
the proprietors of the works, took fright and ran 
off dragging the boat with it, and it was then 
observed, to Mr. Houston's astonishment, that the 
foaming stern surge which used to devastate the 
banks had ceased, and the vessel was carried on 
through water comparatively smooth with a resist- 
ance very greatly diminished. Mr. Houston had 
the tact to perceive the mercantile value of this 
fact to the canal company with which he was 
connected, and devoted himself to introducing 
on that canal vessels moving with this high 
velocity. The result of this improvement was 
so valuable, in a mercantile point of view, as to 
bring, from the conveyance of passengers at a 
high velocity, a large increase of revenue to the 
canal proprietors. The passengers and luggage 


are conveyed 1 in light boats, about sixty feet 
long and six feet wide, made of thin sheet iron, 
and drawn by a pair of horses. The boat starts 
at a slow velocity behind the wave, and at a 
given signal it is by a sudden jerk of the horses 
drawn up on the top of the wave, where it moves 
with diminished resistance, at the rate of 7, 8, 
or 9 miles an hour." 

Scott Russell was not satisfied with a mere 
observation of this kind. He made a magnificent 
experimental investigation into the circumstances. 
An experimental station at the Bridge of Her- 
miston on the Forth and Clyde Canal was arranged 
for the work. It was so situated that there was a 
straight run of 1 500 feet along the bank, and, in 

1 This statement was made to the Royal Society of Edinburgh in 
1837, and it appeared in the Transactions in 1840. Almost before 
the publication in the Transactions the present tense might, alas ! 
have been changed to the past "passengers were conveyed." Is 
it possible not to regret the old fly-boats between Glasgow and 
Ardrossan and between Glasgow and Edinburgh, and their beautiful 
hydrodynamics, when, hurried along on the railway, we catch a 
glimpse of the Forth and Clyde Canal still used for slow goods 
traffic ; or of some swampy hollows, all that remains of the 
Ardrossan Canal on which the horse and Mr. Houston and Scott 
Russell made their discovery ? 


the drawing of it in Scott Russell's paper, three 
pairs of horses are seen galloping along. They seem 
to be galloping on air, but are of course on the 
towing path ; and this remark may be taken as an 
illustration that, if the horses only galloped fast 
enough, they could gallop over the water without 
sinking into it, as they might gallop over a soft 
clay field. That is a sober fact with regard to the 
theory of waves ; it is only a question of time how 
far the heavy body will enter into the water, if it 
is dragged very rapidly over it. This, however, is 
a digression. In the very ingenious apparatus 
of Scott Russell's, there is a pyramid 75 feet 
high, supporting a system of pulleys which carry 
a heavy weight suspended by means of a rope. 
The horses are dragging one end of this rope, 
while the other end is fastened to a boat which 
travels in the opposite direction. It is the old 
principle invented by Huyghens, and still largely 
used, in clockwork. Scott Russell employed it to 
give a constant dragging force to the boat from the 
necessarily inconstant action of the horses. I need 
not go into details, but I wish you to see that 


Scott Russell, in devising these experiments, 
adopted methods for accurate measurement in 
order to work out the theory of those results, the 
general natural history of which he had previously 

I will now read certain results from Scott 
Russell's paper that I think are interesting. The 
depth of the canal at the experimental station 
was about 4 or 5 feet on an average ; it was really 
5 \ feet in the middle, but a proper average depth 
must have been about 4! feet, because Scott 
Russell found by experiment that the natural 
speed of the long wave was about 8 British statute 
miles an hour or 12 feet per second. Here then 
are some of the results. The Rait/i, a boat weigh- 
ing 10,239 Ibs. (nearly 5 tons), took the following 
forces to drag it along at different speeds : at 
472 miles an hour 112 Ibs. ; at 5^92 miles an hour 
261 Ibs. ; and at 6*19 miles an hour 275 Ibs. There 
is no observation at the critical velocity of about 
8 miles an hour. The next is at 9*04 miles an 
hour, and the force is 250 Ibs., as compared with 
275 Ibs. at 6*19 miles an hour. Then at a higher 


speed, IO'48 miles an hour, the force required to 
drag it increases to 268| Ibs. This illustrates that 
water is not a perfect fluid. It also illustrates the 
theoretical result in a beautiful and interesting 
way. If water were a perfect fluid, the forces at 
the lower speeds would be somewhat less than he 
has given, perhaps not very much less : at all 
speeds above 8 miles the force would be nothing ; 
the boat once started, the motion would go on for 
ever. On the same canal another boat, weighing 
12,579 Ibs. (nearly 6 tons), gave these still more 
remarkable results : at 6*19 miles an hour 250 Ibs. ; 
at 7'57 miles an hour 500 Ibs. ; at 8^52 miles an 
hour 400 Ibs. ; and at 9^04 miles an hour only 
280 Ibs. That is a striking confirmation of the 
result of the previous observations. Scott Russell 
says also : " I have seen a vessel in 5 feet water, 
and drawing only 2 feet, take the ground in the 
hollow of a wave having a velocity of about 8 
miles an hour, whereas at 9 miles an hour the keel 
was not within 4 feet of the bottom." Again he 
says : " Two or three years ago, it happened that a 
large canal in England was closed against general 


trade by want of water, drought having reduced 
the depth from 12 to 5 feet. It was now found 
that the motion of the light boats was rendered 
more easy than before ; the cause is obvious. The 
velocity of the wave was so much reduced by the 
diminished depth, that, instead of remaining behind 
the wave, the vessels rode on its summit." He also 
makes this interesting statement : " I am also 
informed by Mr. Smith of Philadelphia, that he 
'distinctly recollects the circumstance of having 
travelled on the Pennsylvania Canal in 1833, when 
one of the levels was not fully supplied with water, 
the works having been recently executed, and not 
being yet perfectly finished. This canal was 
intended for 5 feet of water, but near Silversford 
the depth did not exceed 2 feet ; and Mr. Smith 
distinctly recollects having observed to his astonish- 
ment, that, on entering this portion, the vessel 
ceased to ground at the stern, and was drawn 
along with much greater apparent ease than on 
the deeper portions of the canal." 

Even if one regretted the introduction of rail- 
ways, do not imagine that it can be set forth on 


mechanical grounds that traction in a canal can 
compete for any considerable speeds with traction 
on a railway. Taking again some of the figures 
already given, a boat weighing 10,239 Ibs. required 
112 Ibs., or about i-iooth of its weight, to drag it 
at 4f miles an hour. So that to drag a boat at 
that moderate speed took the same force as would 
be required to drag it on wheels up an incline of 
i in IOO, supposing there to be no friction in the 
wheels on a railway. But at the higher speed of 
9 miles an hour, taking advantage of the com- 
paratively smaller force due to having passed the 
velocity corresponding with the long wave, we have 
250 Ibs., which divided by 10,239 is about I in 40 ; 
so that the force required to drag the boat along 
at the rate of 9 miles an hour was what would be 
required to drag it on wheels up an incline of 
i in 40. Sad to say, I am afraid the wheels have 
it in an economical point of view. 

Ship Waves at Sea. I must now call your 
attention to the most beautiful, the most difficult, 
and in some respects the most interesting part of 


my subject, that is, the pattern of waves formed 
in the rear of a ship at sea, not confined by the 
two banks of a canal. The whole subject of naval 
dynamics, including valuable observations and 
suggestions regarding ship waves, was worked out 
with wonderful power by William Froude ; and the 
investigations of the father were continued by his 
son, Edmund Froude, in the Government Experi- 
mental Works at Haslar, Gun Creek, Gosport. 
William Froude commenced his system of nautical 
experiments in a tank made by himself at Torquay, 
in Devonshire ; first wholly at his own expense for 
several years, and afterwards with the assistance of 
the Government he continued those experiments till 
his death. The Admiralty have taken up the 
work, and have made for it an experimental 
establishment in connection with the dockyard of 
Portsmouth ; and now, after the death of William 
Froude, his son Edmund continues to carry out 
there his father's ideas, working with a large 
measure of his father's genius, and, with his father's 
perseverance and mechanical skill, obtaining results, 
the practical value of which it is impossible to 


over estimate. It is certainly of very great im- 
portance indeed to this country, which depends so 
much on shipbuilding, and the prosperity of which 
is so much influenced by the success of its ship- 
builders, to find the shapes of ships best suited for 
different kinds of work ships of war, swift ships 
for carrying mails and passengers, and goods 
carriers. I may mention also that one of our 
great shipbuilding firms on the Clyde, the Dennys, 
feeling the importance of experiments of this kind, 
have themselves made a tank for experimental 
purposes on the same plan as Mr. Froude's tank 
at Torquay ; and Mr. Purvis, who, when a young 
man, was one of Mr. Froude's assistants, is taking 
charge of that work. The Dennys are going 
through, with their own ships, the series of ex- 
periments which Mr. Froude found so useful, and 
which the Admiralty now find so useful, in regard 
to the design of ships ; and as the outcome of all 
this work a ship can now be confidently designed 
to go at a certain speed, to carry a certain weight, 
and to require a certain amount of horse-power 
from the engine. 


The full mathematical theory of ship waves has 
been exceedingly attractive in one sense, and in 
another sense it has been somewhat repulsive 
because of its great difficulty, for mathematicians 
who have been engaged in hydrodynamical 
problems. Following out that principle of Stokes, 
which was further developed and generalised by 
Lord Rayleigh, we can see how to work out this 
theory in a thorough manner. In fact I can now 
put before you a model [model shown] constructed 
from calculations which I have actually made, by 
following out the lines of theory that I have 
indicated. I find that the whole pattern of waves 
is comprised between two straight lines drawn 
from the bow of the ship and inclined to the wake 
on its two sides at equal angles of 19 28'. It is 
seen in Fig. 48 that two such lines, drawn from 
the bow or front shoulders of the ship, include the 
whole wave-pattern. There is some disturbance 
in the water abreast of the ship, before coming to 
these two lines. Theoretically there is a disturbance 
to an infinite distance ahead and in every direction ; 
but the amount of that disturbance practically is 

VOL. in. I I 


exceedingly small imperceptible indeed until 
you come to these two definite lines. You see the 
oblique wave-pattern waves in echelon pattern. 
The law of that echelon is illustrated by the curves 
shown in Fig. 48. The algebraical equations of 
these curves are 


FIG. 48. Echelon curves. 

where x and j', according to ordinary usage, are 
measured along, and perpendicular to, the direction 
of motion from E towards A, and w is an arbitrary 
variable ; by assuming a series of arbitrary values 
for w, a corresponding series of values for x are 
found from the first equation, and thence the 
corresponding values of y from the second. I 


trace a complete curve thus ABC and ADC ; 
there is a perfect cusp in each curve at B and D 
respectively, although it cannot be shown perfectly 
in the drawing. Another formula, which need not 
be reproduced here, gives a wave-height for every 
point of those curves. Take alternate curves for 
hollows and for crests ; and now in clay or plaster 
of Paris mould a form corresponding with the 
elevation due to the curve AB, plus the elevation 
due to the curve BC, adding the two together; 
thus you get for every point of your curves a 
certain wave-height. With the assistance of Mr. 
Maclean and Mr. Niblett the beautiful clay model 
which is before you has been made, and it shows 
the results of the theory constructed from actual 
calculation. I will tell you how to construct the 
angle of 19 28' made by each of those two straight 
lines AB and AD with the direction of motion CA. 
Draw a circle ; produce the diameter from one end 
to a length equal to the diameter ; and from the 
outer extremity of this projecting line draw two 
tangents to the circle. Each of those tangent 
lines makes an angle of 19 28' with the produced 



diameter, that is, with the wake of the ship or 
with the line of progression of the ship. 

A little more as to the law of this diagram, 
Fig. 48. The echelon waves consist chiefly of the 
very steep waves at a cusp. The theoretical 
formula gives infinite height at the cusp ; but 
that is only a theoretical supposition, though it 
gives an interesting illustration of mathematical 
" infinity." Blur it, or smooth it down, precisely 
as an artist does when he designedly blurs a 
portion of his picture to produce an artistic effect ; 
blur it artistically, correctly, and mathematically, 
and you get the pattern. It will be impossible 
to realise that perfectly ; but I have endeavoured 
to do it in the model, necessarily with an enormous 
exaggeration, however, as you will remark. While 
every other dimension is unchanged, you must 
suppose each wave to be reduced to about a fifth 
part of its height shown in this model ; thus you 
will get the steep " steamboat waves," so much 
enjoyed by the little boys who, regardless of 
danger, row out their boats to them every day 
at the Clyde watering places. Theoretically these 


waves arc infinitely steep ; practically they are so 
steep that the boat generally takes in a little 
water, and is sometimes capsized. There is a 
distance of perhaps a couple of feet from crest to 
crest, and the wave is so steep and " lumpy " on 
the outer border of the echelon that there is 
frequently broken water there fifty or a hundred 
yards from the ship. One point of importance in 
the geometry of this pattern is that each echelon 
cusp, represented in Fig. 48 at B or D, bisects the 
angle between the flank line AB or AD and the 
thwart-ship line BD : the angle in question being 
70 32' (90 -- 19 28'). An observation of this 
angle was actually made for me by Mr. Purvis. 
He observed, from the towing of a sphere instead 
of a boat (so as to get a more definite point), the 
angle between the flank line AB and the direction 
of motion CA, and found it to be 19^. The 
theoretical angle is 19 28', and we have therefore 
in this observation a very admirable and interest- 
ing verification of the theory. 

The doctrine embodied in the wave-model may 
be described in a very general way thus. Think 


of a ship travelling over water. How is it that 
it makes the wave ? Where was the ship when 
it gave rise to the wave BCD in Fig. 48 ? Answer : 
the portion BCD of the wave-pattern is due to what 
the ship did to the water when the ship was at 
E, the point E being at the same distance behind 
C that the point A is in front of C ; when it was 
at E it was urging the water aside, and the effect 
of the ship pushing the water aside was to leave a 
depression. Now suppose the ship to be suddenly 
annihilated or annulled, what would be the result ? 
The waves would travel out from it, as in the case 
of a stone thrown into the water. Again suppose 
the ship to move ten yards forward and then stop, 
what would be the result ? A set of waves travel- 
ling forward w r hile the disturbance that the ship 
made by travelling ten yards remains. Now 
instead of stopping, let the ship go on its course : 
the wave disturbance is going its course freed 
from the ship, and travels forward. When the 
disturbance originated which has now reached 
any point C, the ship was as far behind that 
point C as it now is before it. Calculate out the 


result from the law that the group-velocity is half 
the wave-velocity the velocity of a group of 
waves at sea is half the velocity of the individual 
waves. Follow the crest of a wave, and you see 
the wave travelling through the group, if it forms 
one of a group or procession of waves. Look, 
quite independently of the ship, at a vast pro- 
cession of waves, or imagine say fifty waves ; look 
at one of those waves, follow its crest ; in imagina- 
tion fly as a bird over it, keeping above the crest 
as a bird in soaring does sometimes, and, begin- 
ning over the rear of the procession, a hundred 
yards on either side of the ship's wake, you will 
find the waves get larger and larger as you go 
forwards. Then go backwards through the pro- 
cession, and you will see the waves get smaller 
and smaller and finally disappear. You have now 
gone back to the rear of the procession ; a small 
wave increases and travels uniformly forward, and, 
while the crest of each wave always goes on with 
the velocity corresponding to the length of the 
wave, the rear of the procession travels forward 
at half the speed of the wave : so that every wave 


is travel-ling forward through the procession from 
its rear at a speed which is the same relatively to 
the rear of the procession as the speed of the 
rear of the procession relatively to the water- 
Thus each separate wave is travelling at the ship's 
speed, \vhich is twice as fast relatively to the 
water as the rear of the procession of waves is 
travelling. The wave is the progression of a 
form ; the velocity of a wave is clearly intelligible ; 
the velocity of a procession of waves is still another 
thing. The penetrating genius of Stokes originated 
the principle, admirably worked out by Osborne 
Reynolds and Lord Rayleigh, who have given us 
this in the shape in which we now have it. 

Now I must call your attention to some exceed- 
ingly interesting diagrams l that I am enabled to 
show you through the kindness of Mr. \Y. II 
White, director of Naval Construction for the 
Admiralty, and Mr. Edmund Froude, to whose 

1 All these diagrams, together with those from Scott Russell's 
paper, are reproduced in the Minutes of Proceedings of the Institu- 
tion of Mechanical Engineers, August 3, 1887. 


work I have already referred. Fig. 12, Plate 82, 
shows a perspective vie\v of echelon waves taken 
from Mr. William Froude's paper, " Experiments 
upon the Effect Produced on the Wave-making 
Resistance of Ships by Length of Parallel Middle 
Body''' {Institution of Naval Architects, vol. xviii. 
1877, page 77). 

The three diagrams from Mr. White, Figs. 6, 7, 
and 8, Plate Si, show profiles of the thwart- ship 
waves of various ships, at different speeds. Look 
first at Fig. 6, showing *.the wave profile for 
H.M.S. Curlew at a speed of nearly 15 knots an 
hour. Note how the water, after the first eleva- 
tion, dips down below the still-water line ; rises up 
to a ridge at a distance back from the first nearly 
but not exactly equal to the wave-length corre- 
sponding with the speed ; and then falls down 
again, experiencing various disturbances. From 
the appearance of the waves raised by ships going 
at high speeds, we may learn to tell how quickly 
they are going. The other day, at the departure 
of the fleet from Spithead after the great naval 
review, a ship was said to be going at 18 knots, 


while it was obvious from the waves it made that 
it was not going more than 12. In Fig. 7 we have 
wave profiles for another ship at two different 
speeds. The upper line corresponds to a speed 
of 1 8*4 knots ; the lower line to a speed of 17 
knots. In the first case the water shoots up to 
its first maximum height close to the bow, sinks 
to a minimum towards midships, and flows away 
past the stern slightly above still-water level. In 
the second case the character of the wave is some- 
what similar, but smaller in height ; and there is a 
marked difference at the stern, due to other dis- 
turbing causes. In Fig. 8 we have three different 
speeds for H.M.S. Orlando similarly represented. 

There is still another very interesting series of 
diagrams, Figs. 13 to 19, Plates 83 and 84, taken 
from Mr. Edmund Froude's paper " On the Lead- 
ing Phenomena of the Wave-making Resistance 
of Ships," read before the Institution of Naval 
Architects, 8th April, 1881. In Figs. 13 to 17 
are shown the waves produced by a torpedo 
launch at speeds of 9, 12, 15, 18, and 21 knots per 
hour. We need not here go into the law of wave- 



length, but I may tell you that it is as the square of 
the velocity : the wave-length is four times as great 
for 1 8 as for 9 knots. Look now at the pattern 
of the waves in Figs. 9, (48 above), and 10, Plate 
82. Look at the echelon waves and the thwart- 
ship waves. Mr. Froude had not worked out the 
theory that has given the curvature of the trans- 
verse ridge exactly ; but he drew the waves from 
general observation, and it is wonderful to see 
how nearly they agree with the theoretical curves, 
Fig s - 9> (4-8 above), and the model, Fig. 10. 


Velocity of Wave. 
Knots per hour. 

Length of Wave 

Velocity of Wave. 
Kno:s per hour. 

Length of Wave. 








1 80 


35 & 


2O I 


45' 1 












79 -6 




94 '4 






5 i 





16 142 



That is a most interesting series of diagrams in 


Plates 83 and 84, and as a lesson it conveys more 
than any words of mine. 

Here is a table (page 491) giving the length of a 
free wave ; and remember, when once the waves 
are made and are left by the ship, they are then 
and thereafter free waves. At 6 knots per hour 
the wave-length is 19^9 feet ; at 12 knots it is four 
times as great. At 10 knots it is 54 feet ; at 20 it 
is four times as much. The greatest speeds in 
Froude's diagrams give about 240 feet length of 
wave. Now that is a very critical point with 
respect to the length of the wave and the speed of 
the ship. I may tell you that Froude the elder 
and his son Edmund have made most admirable 
researches in this subject, and have poured a flood 
of light on some of the most difficult questions of 
naval architecture. 

Parallel Middle Body. I should like to say 
something about the practical question of parallel 
middle body. When I first remember shipbuilding 
on the Clyde, and its progress towards its present 
condition, a very frequent incident was that when 


a ship was floated it was found to draw too much 
water forward, in other words to be down by the 
head. When this happened, the ship was taken 
out of the water again, and a parallel piece, 
I o or 20 or 30 feet long, was put into the middle : 
a parallel middle body, curved transversely, but 
with straight lines in the direction of its length. 
Many a ship was also lengthened with a view to 
add to its speed. William Froude took up the 
question of parallel middle body, and the effect of 
the entrance and run. The entrance is that part of 
the ship forward, where it enters the water and 
swells out to the full breadth of the ship ; the run 
is the after part, extending from where the ship 
begins to narrow to the stern. A ship may consist 
of entrance, parallel middle body, and run. Froude 
investigated the question, Is the parallel middle 
body inserted in a ship an advantage or a dis- 
advantage, in some cases or in all cases ? He 
found it a very complex question. According to 
the relation of the wave-length to the length of the 
ship, it produces a good or a bad effect. A ship 
with a considerable length of parallel middle body 


shows very curious phenomena regarding the 
resistance at different speeds. As the speed is 
raised, the resistance increases; but on a further 
increase of speed, it seems as if it was beginning 
to diminish ; the resistance never quite diminishes 
however with increase of speed, but only increases 
much less rapidly. The curve indicating the 
relation of the speed to the velocity has a succes- 
sion of humps or rises, each showing a rapid 
increase of resistance ; between these it becomes 
almost flat, showing scarcely any increased resist- 
ance. Froude has explained that thoroughly by 
the application of this doctrine of ship waves which 
I have endeavoured to put before you. When the 
effect of the entrance or bow, and the effect of the 
run or stern, are such as to annul or partially to 
annul each other's influence in the production of 
waves, then we have a favourable speed for that 
particular size and shape of ship. On the other 
hand, when the crest of a wave astern due to the 
action of the bow agrees with the crest of a wave 
astern due to that of the stern, then we have an 
unfavourable speed for that particular size of ship. 


Thus Froucic worked out a splendid theory, 
according to which, for the speed at which a ship 
is to go, a certain length of parallel middle body 
may, if otherwise desired, be an advantage. But 
on the whole the conclusion was that if the ship 
is equally convenient, if it is not too expensive, if 
it can pass through the lock gates, &c., and if all 
the other practical conditions can be fulfilled, 
without a parallel body it is better that the ship 
should be all entrance and run, according to 
Newton's form of least resistance : fine lines for- 
ward, swelling out to greatest breadth amidships 
and tapering finely towards the stern. In other 
words, the more ship-shape a ship is, the better. 

I wish to conclude by offering one suggestion. 
I must premise that, when I was asked by the 
Council to give this lecture, I made it a condition 
that no practical results were to be expected from 
it. I explained that I could not say one word 
to enlighten you on practical subjects, and that 
I could not add one jot or tittle to what had 
been done by Scott Russell, by Rankinc, and by 


the Froudes, father and son, and by practical men 
like the Dennys, W. H. White, and others ; who 
have taken up the science and worked it out in 
practice. But there is one suggestion founded on 
the doctrine of wave-making, which I venture to 
offer before I stop. I have not explained how 
much of the resistance encountered by a ship in 
motion is due to wave-making, and how much to 
what is called skin resistance. I can briefly give 
you a few figures on this point, which have been 
communicated to me by Mr. Edmund Froude. 
Fora ship A, 300 feet long and 3I-J feet beam and 
2634 tons displacement, a ship of the ocean mail 
steamer type, going at 13 knots an hour, the skin 
resistance is 5 '8 tons, and the wave resistance 3*2 
tons, making a total of 9 tons. At 14 knots the 
skin resistance is but little increased, namely 6'6 
tons; while the wave resistance is nearly double, 
namely 6' 15 tons. Mark how great, relatively to 
the skin resistance, is the wave resistance at the 
moderate speed of 14 knots for a ship of this size 
and of 2634 tons weight or displacement. In the 
case of another ship B, 300 feet long and 46*3 feet 


beam and 3626 tons displacement a broader and 
larger ship with no parallel middle body, but with 
fine lines swelling out gradually the wave resist- 
ance is much more favourable. At 13 knots the 
skin resistance is rather more than in the case of 
the other ship, being 6'95 tons as against 5 '8 tons ; 
while the wave resistance is only 2*45 tons as 
against 3*2 tons. At 14 knots there is a very re- 
markable result in this broader ship with its fine 
lines, all entrance and run and no parallel middle 
body: at 14 knots the skin resistance is 8 tons 
as against 6'6 tons in ship A, while the wave resist- 
ance is only 3*15 tons as compared with 6*15 tons. 
Another case which I can give you is that of a 
torpedo boat 125 feet long, weighing 51 tons. At 
a speed of 20 knots an hour the skin resistance 
is i'2 ton, and the wave resistance ri ton ; total 
resistance 2*3 tons. To calculate the horse-power 
you multiply the speed in knots per hour by 6f , 
and then multiply the resistance in tons by the 
product so obtained ; and the result for the 
torpedo boat going at 20 knots an hour is 307 
horse-power to overcome a resistance of 2*3 tons 
VOL. ill. K K 


or i-22nd of her weight (5 1 tons). Again the 
ship B of 300 feet length, going at 20 knots an 
hour with an expenditure of 4550 horse-power, 
experiences a resistance of 34 tons, or about 
i-noth of her weight (3626 tons). Thus the 
energy actually expended in propelling these 
vessels at 20 knots an hour at sea would be 
sufficient, if the}* were supported on frictionless 
wheels, to drag them at the same speed up railway 
inclines, of I in 22 for the torpedo boat, and I in 
no for the ship B. 

My suggestion is this, and I offer it with exceed- 
ingly little confidence, indeed with much diffidence ; 
but I think it is possibly worth considering. Inas- 
much as wave resistance depends almost entirely on 
action at the surface of the water, and inasmuch 
as a fish swimming very close to but below the 
surface makes very little wave disturbance, it seems 
to me that by giving a great deal of body below 
the water line we may relatively diminish the wave 
disturbance very much. To get high speeds of 18 
and 20 knots an hour, it is probable that, by swell- 
ing out the ship below like the old French ships 

ay SHIP WA VES. 499 

instead of having vertical sides making the 
breadth of beam say five feet more below the 
water than at the water line there may be 
obtained a large addition to the displacement 
or carrying power of the ship, with very little 
addition to the wave disturbance, and therefore, 
with very little addition to the wave resistance, 
which is most important at high speeds. I think 
it may be worth while to consider this in regard to 
the designs of ships. 

In conclusion, I should like to urge you to 
look at these phenomena for yourselves. Look 
at the beautiful wave-pattern of capillary waves, 
which you will find produced by a fishing line 
hanging vertically from a rod, or from an oar, or 
from anything carried by a vessel moving slowly 
through smooth water at speeds of from about -J- 
knot to 2 knots an hour. Again, look at the 
equally beautiful wave-pattern produced by ships 
and boats, as illustrated in Fig. 48. But you 
can scarcely see the phenomena more beautifully 
manifested than by a duck and ducklings. A full 

K K 2 


sized duck has a splendidly shaped body for de- 
veloping a wave-pattern, and going at good speed 
it produces on the surface of a pond very nearly 
the exact pattern of ocean waves. A little duck- 
ling going as fast as it can, perhaps about a knot 
an hour, shows very admirably the capillary 
waves, 1 differing manifestly from the ocean waves 
formed in the front and at the rear of a larger 
body moving more rapidly through the open water. 
I call attention to this, because, having given you 
perhaps a rather dry statement of scientific facts, 
if I can say a word that will lead you each to use 
your eyes in looking at ships, boats, ducks, and 
ducklings, moving on water at different speeds, 
and to observe these beautiful phenomena of 
waves, I think, even were you to remember nothing" 
of this lecture, you would have something to keep 
in your minds for the rest of your lives. 

1 For information regarding capillary waves, see Scott Russell's 
Report on Waves (British Association, York, 1844, pp. 311-390) ; 
also Parts III., IV., and V of Sir William Thomson's paper, 
"Hydro-Kinetic Solutions and Observations" (Philosophical 
Magazine, November 1871). 




\_Bcingan account by Captain Creak, R.N ,F.R.S., of observa- 
tions made subsequently to those described on pp. 255-266.] 

II. M. surveying vessel Penguin visited Cossack 
on November 3rd, 1890, reaching the anchorage 
without disturbance of either compass or dipping 
needle, although such might have been expected 
from the experience of the Meda on a previous 
occasion in 1885. Observations of the magnetic 
elements were made with absolute instruments at 
different stations on shore, but these showed little 
or no disturbance from normal values. 

On the 5th inst., when proceeding to sea with 
Bezout Island bearing S. 79 W., distance 2 miles, 
the north point of the compass was suddenly 
deflected two points to the westward. The ship 
was immediately anchored, and some hours of the 
next day were spent in examining this anchor- 
age and neighbourhood, the soundings giving 
9 fathoms throughout. Observations were also 


made during this time on Bezout Island (the 
nearest visible land), of the absolute values of 
the three magnetic elements. The results were 

The instruments employed on board the ship 
were the Standard compass, situated 68 feet above 
the bottom of the sea, and a Fox dip circle about 
6 feet higher. 

It was found that the centre of disturbance was 
about 50 feet in diameter, and drifting slowly 
over it from N.W. to S.E. three or four times, the 
greatest disturbance experienced was from a force 
repelling the north-seeking end of the needle, 
amounting to 23 when on the N.W. side of the 
centre, to 55 on the S.E. side. 

The ship was anchored for four hours nearly over 
the centre of disturbance, the north-seeking end of 
the compass needle remaining constantly repelled 
as much as from 50 to 55. When exactly over 
the centre the observed inclination or dip was 83 S., 
the normal value for the general locality being to 
the nearest degree 50 S. At this time the com- 
pass showed but little disturbance. 

These large values of 55 in the declination and 
33 in the inclination were confined to a very small 
area, the values of the disturbance in both elements 
decreasing rapidly as the centre was passed in any 
direction. It was considered, from the observa- 
tions made, that the whole area of disturbance 
covered a space of one square mile. 


The position of the Penguin' 's centre of disturb- 
ance was Bezout Island (Beacon on summit) 
S. 79} W. (true), distance 2-14 miles. This 
point is 1*3 miles from the Medas centre of dis- 

One general result derived from the CJiallenget 
and other observations, that in places north of the 
magnetic equator local disturbances are caused by 
an excess of blue magnetism above the normal, 
and south of that equator an excess of red mag- 
netism, receives additional confirmation from the 
Penguin s observations at Cossack. Such an 
excess of red magnetism as at Cossack is at least 
very abnormal, but the results were obtained with 
great care and attention to detail. 



ACCOUNT, 3, 107 

Admiralty standard compass, 

283, 286 

Airy, Sir George, 209, 217-223 
Altitude, 71, 81 
Anchor Line, 379 
Anchi/tia, 379 
Anderson, Sir James, 113, 114, 

383, 441 
Astronomical navigation, 3, 

Atlantic cables, descriptions of, 

Azimuth compass, 3, 11-27, 57, 

67, 335 

mirror, 329-336 

BAY FIELD, Captain, 49 note 
Bearings, u, 329-336 
Beechy, Admiral, lutes in Eng- 
lish Channel, 168 
Bel knap, Commander, 356, 


\\ >urd of Northern Lights, 390 
Bottomley, William, 322 note 
Brake on sounding machine, 

354, 356, 365, 372, 374 
Britannitt 378 

British statute mile, 74, 422 

CABLES, laying and lifting deep- 
sea, 422-449 

Cachopo shoals, 59 61 

Cagniard de la Tour, 131 

Cardwell, Lord, 255 

Castor-pulley, 348, 349 

Cavendish, 154 

Celestial pole, 12, 71, 82 

Challenger, H.M.S., 359, 503 

Chart of English Channel, 385 

Charts, 27-32 

Chemical sounding tubes, 381, 

Chronometer, 3, 33-42, 85 

Clark, Latimer, 365 

Clyde Navigation Trustees, 216 

Collet, Captain, 322 note 

C llinson, Sir Richard, 420 

Collisions, regulations for pre- 
venting, 116-125 

Colomb, Captain, 125, 126, 128, 

Commissioners of Irish lights, 

Compass, Admiralty, 283, 284 
antiquity of, 229-232 
azimuth, 3, 11-27, 57, 67, 

card, 19, 278-281, 285-302 



Compass, correction of, 303-329 
description of, 25-2,7, 277- 


early mentions of, 232-235 
influence of land on 

manner's, 255-266, 501- 

503 . 

magnetising needle, 238 
method of suspending in 

water, 236-238 
variation of, 24, 254, 267, 

Compensation of chronometer, 


Continuous sounding, 380, 381, 
^ 386-388 
Coulomb, 248 
Creak, Captain, 257, 261-267, 

50I-5 3 

Crondace, Captain, 125, 126,128 
Curlew, H.M.S., 489 

DARWIN, George, 158, 189 

Horace, 158 

Dead reckoning, 3, 105-112 
Declinational tide, 175 
Deep-sea lead, 49, 52, 365 

sounding, 3, 112-116, 337- 


Deflector, the, 322-329 
Denny, experimental tank, 480, 

496 ^ 

Depth recorder, 54, 375, 376, 381 
Devonia, 379, 380 
Dioptric system in lighthouses, 


Dip, 24, 249, 278 
Dipping-needle, 21, 278 
Disk-globe-and cylinder integra- 
tor, 177 
Dover, Straits of, influence of, 

on tides, 201-204 
Duperry, 267 

EARNSHAW, Thomas, 35, 38 
Earth, figure of, 68-70 

Earth, observations of continual 
palpitation of, 158-159 

Eastern Province, loss of, 256 

Echelon curves, 482 

Eclipsing lights, 395 

Edington, Captain, 361 

Equilibrium theory of the tides, 
160, 163, 224-227 

Erichsen's self-registering lead, 

Evans, Captain, 204, 207, 266 
Sir Frederic, 140, 175, 1 88 

FARADAY, 21, 246, 267 
Faraday, 352 
Fixed lights, 395, 396, 397 
Flashing lights, 395, 396 
Flinders bar, 312-320 
Fly-boats on Canals, 470-473 
Plying soundings, 362, 369-371 
Fronde, 289, 368. 479, 480, 488- 

GAS, use of in lighthouses, 417 

Gauss, 270 

Gilbert, Dr., 240, 242, 253, 266, 

^ 285, 335 

Glasses, 47-49 

Gravitation, 154, 159, 191 

variation of, due to lunar 

disturbance, 158 
Gray, 124, 159, 369 
Great Eastern, 435, 440-442 
Gridiron pendulum, 37, 38 
Group flashing light, 400 
Guiot of Provence's experiment. 
234, 235 

HALI.EY, 271 

Hardiness of sounding wire, 380 
Harmonic analyser, 178 
Harris, Captain, 175 
Harrison, John, 35, 37, 38, 98 
Hartnup, 38-42 



Hedderwick, Captain, 379 
Henry, Professor, 122, 131 
Herschel, Sir John, 17 
Holmes' rescue light, 134-138 
Hoofer, 349, 360, 361, 363, 368, 


Hopkinson, 400 
Horizon, 72, 73 

dip of, 6, 77, 82 

to find distance of, 76, 77 
Huyghens, 474 

INERTIA, 191, 193, 352 
Irish Channel, tides in, 168 
Iron Duke, 1 08 

TENKIN, Professor, 358, 371 
Johnson, Messrs., 341, 343 

KERR, Captain Lord Walter. 

Key, Admiral Sir Cooper, 160, 


Lalla Rookh, 96, 337, 383, 385 
Laplace, theory of the tides, 

160, 168, 169, 213 
Latitude, 72, 82-85 

by Sumner's method, 94 
Leighton, Captain, 382 
Lighthouse characteristics, 389- 


Lochman, 245 
Log, 42-47 

ground, 46, 47 

Massey, 4, 46, 48 
Longitude, 35-37, 72, 85 
Luminiferous ether, 78 note 
Lunars, 78, 8 1, 85, 98 
Lushington, Profess jr, 17 note 

MAGNETIC charts, 22, 23 
meridians, 21 

Magnetic north, 20 

poles, 22, 24 
Magneti-ing magnet, 238 
Massey log, 4, 46, 48, 108 

sounding fly, 49-51, 114 
Afeda, H.M.S., 260263, 5<>i- 

M creator's projection, 29-32, 


Meridian, 71 
Mile, nautical, 45, 73, 74, 422 

British statute, 74, 422 
Minotaur, H.M.S., 386 
Moon, influence of, on weather, 
1 88 
attraction of, on water of 

earth, 150, 154, 194 
Moriarty, Captain, 93, 1:3,221, 


Morse Colomb flashing alpha- 
bet, 400 

alphabet generalized, 130, 

Munro, Captain, 379 

Nautical Almanac, 3, 83 and 
note, 85, 88, 103 

Navigation defined, i, 2 
astronomical, 3, 68-105 

Neap tides, 161-163 

Newton, Sir Isaac, 4, 35, 98, 
99, 153. 191-198 

Norman, Robert, 249, 273, 278 

North celestial pole, 12 
magnetic pole, 22, 25 
terrestrial pole, 12, 25 

OCCULTING lights, 395, 397 
Orbis virtutis of Gilbert, 246 
Orlando, H.M.S., 490 

Palm, 382 

Parallel middle body, 492-495 

Paranese, 361 



Penguin, H.M.S, 501-503 
Pianoforte wire, sounding by, 
51, 114-115- 337-388 

splicing, 341-343. 354 
Pilotage, 3, 55-68 
Polaris, 12, 13, 82, 83 
Polarity, 244 
Pole, celestial, 12, 71, 82 

magnetic, 22, 25, 252 

terrestrial, 12, 25 
Portland, race of, 141 
Precession of the equinoxes, 


Preece, W. H., 400, 401, 419 
Price Edwards, 394, 421 
Prime vertical, 70 
Pyramids and pole-star, 15-17 

Siemens, 352, 366 
Signalling, 125 

by sound, 395, 420, 421 
Siren, 131-134, 420, 421 
Smith, Archibald, 255, 257 
Solar tides, 149 

Sounding machine, 52, 350, ^51, 

by pianoforte wire, 51, 114, 
"5, 337-388 

tubes, 381, 382 
Spring tides, 161, 163 
Station pointer, 3, 32, 33 
Steerage, errors in, 108-110 
Stokes, Sir George, 462, 463, 

481, 488 
Simmer's method, 87-98 

RADIAN, defined, 20 note, 365 


Rankine, 495 
Raper, Lieutenant, 44 note, 48, 

49, 10 3 
Rayleigh, Lord. 462, 463, 481, 


Refraction of light, 78, 102 
Regulations for preventing col- 
lisions, 116-125 
Rescue light, Holmes', 134-138 
Revolving lights, 395, 396 
Reynolds, Professor Osborne, 

123, 462, 463, 488 
Rule of the road, 121 
Russell, John Scott, 452-478, 


Rust of sounding wire, prevent- 
ing, 363-365. 378 

SABTNE, Sir Edward, 267, 322, 


Seamanship, I 

Sextant, 3, 4-11, 66, 67, 84, loo 
Seymour, Admiral Beauchamp, 

Ship-waves, 450-500 

Terella, 246 

Thompson, Captain, 378 
Thomson, Professor James, 177, 


Tidal current, the, 140 
wave, 142 
analy-is, 209-223 
Tide gauge, 171, 214-216 

generating force, 154-157, 

1 60, 194-198 
predicter, 184 
Tides, declinational, 175 
defined, 142-144 
double high and low, 141, 

early knowledge of, 150- 


effect of atmospheric pres- 
sure on, 147-149 
elastic, 198-201 
equilibrium theory of, 1 60, 

163, 224-227 
lunar, 150, 154 
mean solar diurnal, 147 
meaning both horizontal 
and vertical motions of 
water, 140 


Tides, nenp, 161-163 

solar, 149 

spring, 161, 163 
Trinity Board, 390 
Triple flashing light, 402 
T>ndall, Professor, 123, 133 

I'an-uant, 1 08, 133 
Variation, 24, 254, 267, 272-274 
Velocity of waves 457, 458,491 
Vertical, prime, 70 
Viscosity of water, 454-457* 

460-462, 466 
Vyse, Colonel Howard, 17 

WAVES, ship, 450-500 
Webster and Horsfall, 343, 344, 


Wharton, Captain, 261 
White Star Line, 378 
White, Mr. W. IL, 488, 489, 

V\ ind, generation of currents 

by, I44-M7 

YOUNG, James, 364 



AND TRIGONOMETRY. By J. H. PALMER, Head Schoolmaster, R.N, 
Gl. ; 



Professor of Natural Philosophy in the University of Glasgow. 

Second Edition. 8vo. iSs. 


Crown 8vo, 6s. 


3 Vols. Illustrated. Vol.1. CONSTITUTION OF MATTER. 


H..M.S. Catnbtid^e, Devonport. Gl. 8vo. 45. 6 J. 


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